显示找到的9个结果中的1-9个。
第页1
4, 6, 6, 8, 8, 9, 8, 10, 8, 12, 8, 12, 8, 12, 12, 12, 8, 12, 8, 16, 12, 12, 8, 15, 12, 12, 10, 16, 8, 18, 8, 14, 12, 12, 16, 16, 8, 12, 12, 20, 8, 18, 8, 16, 16, 12, 8, 18, 12, 18, 12, 16, 8, 15, 16, 20, 12, 12, 8, 24, 8, 12, 16, 16, 16, 18, 8, 16, 12, 24, 8, 20
配方奶粉
求和{k=1..n}a(k)~(15*n*(log(n)+2*gamma-1)+n*(5*log(2)+3*logA001620号.
数学
表[DivisorSigma[0,6*n],{n,1,150}]
交叉参考
囊性纤维变性。A000005号,A001620号,A099777号,A372713型,A372784飞机,A372785型,A372787飞机,A372788飞机,A372789型,A372790型,A372791型,A372792飞机.
3, 6, 4, 9, 6, 8, 6, 12, 5, 12, 6, 12, 6, 12, 8, 15, 6, 10, 6, 18, 8, 12, 6, 16, 9, 12, 6, 18, 6, 16, 6, 18, 8, 12, 12, 15, 6, 12, 8, 24, 6, 16, 6, 18, 10, 12, 6, 20, 9, 18, 8, 18, 6, 12, 12, 24, 8, 12, 6, 24, 6, 12, 10, 21, 12, 16, 6, 18, 8, 24, 6, 20, 6, 12, 12
配方奶粉
Sum_{k=1..n}a(k)~(21*n*(log(n)+2*gamma-1)+n*6*log(3))/9,其中gamma是欧拉-马斯切罗尼常数A001620号.
数学
表[DivisorSigma[0,9*n],{n,1,150}]
交叉参考
囊性纤维变性。A000005号,A099777号,A372713型,A372784飞机,A372785型,A372786飞机,A372787飞机,A372788飞机,A372790型,A372791型,A372792飞机.
6, 8, 9, 10, 12, 12, 12, 12, 12, 16, 12, 15, 12, 16, 18, 14, 12, 16, 12, 20, 18, 16, 12, 18, 18, 16, 15, 20, 12, 24, 12, 16, 18, 16, 24, 20, 12, 16, 18, 24, 12, 24, 12, 20, 24, 16, 12, 21, 18, 24, 18, 20, 12, 20, 24, 24, 18, 16, 12, 30, 12, 16, 24, 18, 24, 24
评论
通常,对于m>=1,求和{j=1..n}τ(m*j)=A018804号(m) *n*log(n)+O(n)。
如果p是素数,则求和{j=1..n}tau(p*j)~(2*p-1)*n*(log(n)-1+2*gamma)/p+n*log(p)/p,其中gamma是Euler-Mascheroni常数A001620号.
配方奶粉
求和{k=1..n}a(k)~(40*n*(log(n)+2*gamma-1)+n*(20*log(2)+8*logA001620号.
数学
表[DivisorSigma[0,12*n],{n,1,150}]
交叉参考
囊性纤维变性。A000005号,A099777号,A372713型,A372784飞机,A372785型,A372786飞机,A372787飞机,A372788飞机,A372789型,A372790型,A372791型.
3, 4, 6, 5, 6, 8, 6, 6, 9, 8, 6, 10, 6, 8, 12, 7, 6, 12, 6, 10, 12, 8, 6, 12, 9, 8, 12, 10, 6, 16, 6, 8, 12, 8, 12, 15, 6, 8, 12, 12, 6, 16, 6, 10, 18, 8, 6, 14, 9, 12, 12, 10, 6, 16, 12, 12, 12, 8, 6, 20, 6, 8, 18, 9, 12, 16, 6, 10, 12, 16, 6, 18, 6, 8, 18, 10
配方奶粉
求和{k=1..n}a(k)~(8*n*(log(n)+2*gamma-1)+n*4*log(2))/4,其中gamma是Euler-Marcheroni常数A001620号.
数学
表[DivisorSigma[0,4*n],{n,1,150}]
交叉参考
囊性纤维变性。A000005号,A099777号,A372713型,A372785型,A372786飞机,A372787飞机,A372788飞机,A372789型,A372790型,A372791型,A372792飞机.
2, 4, 4, 6, 3, 8, 4, 8, 6, 6, 4, 12, 4, 8, 6, 10, 4, 12, 4, 9, 8, 8, 4, 16, 4, 8, 8, 12, 4, 12, 4, 12, 8, 8, 6, 18, 4, 8, 8, 12, 4, 16, 4, 12, 9, 8, 4, 20, 6, 8, 8, 12, 4, 16, 6, 16, 8, 8, 4, 18, 4, 8, 12, 14, 6, 16, 4, 12, 8, 12, 4, 24, 4, 8, 8, 12, 8, 16, 4, 15
配方奶粉
求和{k=1..n}a(k)~(9*n*(log(n)+2*gamma-1)+n*log(5))/5,其中gamma是Euler-Marcheroni常数A001620号.
数学
表[DivisorSigma[0,5*n],{n,1,150}]
交叉参考
囊性纤维变性。A000005号,A099777号,A372713型,A372784飞机,A372786飞机,A372787飞机,A372788飞机,A372789型,A372790型,A372791型,A372792飞机.
2, 4, 4, 6, 4, 8, 3, 8, 6, 8, 4, 12, 4, 6, 8, 10, 4, 12, 4, 12, 6, 8, 4, 16, 6, 8, 8, 9, 4, 16, 4, 12, 8, 8, 6, 18, 4, 8, 8, 16, 4, 12, 4, 12, 12, 8, 4, 20, 4, 12, 8, 12, 4, 16, 8, 12, 8, 8, 4, 24, 4, 8, 9, 14, 8, 16, 4, 12, 8, 12, 4, 24, 4, 8, 12, 12, 6, 16, 4
配方奶粉
求和{k=1..n}a(k)~(13*n*(log(n)+2*gamma-1)+n*log(7))/7,其中gamma是Euler-Marcheroni常数A001620号.
数学
表[DivisorSigma[0,7*n],{n,1,150}]
交叉参考
囊性纤维变性。A000005号,A099777号,A372713型,A372784飞机,A372785型,A372786飞机,A372788飞机,A372789型,A372790型,A372791型,A372792飞机.
4, 5, 8, 6, 8, 10, 8, 7, 12, 10, 8, 12, 8, 10, 16, 8, 8, 15, 8, 12, 16, 10, 8, 14, 12, 10, 16, 12, 8, 20, 8, 9, 16, 10, 16, 18, 8, 10, 16, 14, 8, 20, 8, 12, 24, 10, 8, 16, 12, 15, 16, 12, 8, 20, 16, 14, 16, 10, 8, 24, 8, 10, 24, 10, 16, 20, 8, 12, 16, 20, 8, 21
配方奶粉
求和{k=1..n}a(k)~(20*n*(log(n)+2*gamma-1)+n*12*log(2))/8,其中gamma是Euler-Marcheroni常数A001620号.
数学
表[DivisorSigma[0,8*n],{n,1,150}]
交叉参考
囊性纤维变性。A000005号,A099777号,A372713型,A372784飞机,A372785型,A372786飞机,A372787飞机,A372789型,A372790型,A372791型,A372792飞机.
2, 4, 4, 6, 4, 8, 4, 8, 6, 8, 3, 12, 4, 8, 8, 10, 4, 12, 4, 12, 8, 6, 4, 16, 6, 8, 8, 12, 4, 16, 4, 12, 6, 8, 8, 18, 4, 8, 8, 16, 4, 16, 4, 9, 12, 8, 4, 20, 6, 12, 8, 12, 4, 16, 6, 16, 8, 8, 4, 24, 4, 8, 12, 14, 8, 12, 4, 12, 8, 16, 4, 24, 4, 8, 12, 12, 6, 16
配方奶粉
Sum_{k=1..n}a(k)~(21*n*(log(n)+2*gamma-1)+n*log(11))/11,其中gamma是欧拉-马斯切罗尼常数A001620号.
数学
表[DivisorSigma[0,11*n],{n,1,150}]
交叉参考
囊性纤维变性。A000005号,A099777号,A372713型,A372784飞机,A372785型,A372786飞机,A372787飞机,A372788飞机,A372789型,A372790型,A372792飞机.
与和{k=1..n}τ(m*k)的渐近展开有关的序列。
+10 0
1, 2, 3, 16, 5, 864, 7, 4096, 729, 64000, 11, 6879707136, 13, 2809856, 61509375, 4294967296, 17, 812479653347328, 19, 26843545600000000, 26795786661, 2791309312, 23, 4019988717840603673710821376, 9765625, 73719087104, 7625597484987, 25962355635465062711296, 29
评论
对于m>=1,求和{k=1..n}τ(m*k)=A018804号(m) *n*log(n)+O(n)。
如果p是素数,则求和{k=1..n}tau(p*k)~(2*p-1)*n*(log(n)-1+2*gamma)/p+n*log(p)/p,其中gamma是Euler-Mascheroni常数A001620号.
配方奶粉
Sum_{k=1..n}τ(m*k)~A018804号(m) *n*(对数(n)-1+2*伽马)/m+n*对数(a(m))/m。
a(m)=exp(极限{n->oo}(m*(和{k=1..n}τ(m*k))-A018804号(m) *n*(对数(n)-1+2*伽马))/n)。
如果p是素数,那么a(p)=p。
如果p是素数,那么a(p^k)=p^(k*p^)(k-1))。
如果p和q是不同的素数,那么a(p*q)=p^(2*q-1)*q^(2*p-1)。
例子
求和{k=1..n}τ(4*k)~(8*n*(log(n)+2*gamma-1)+n*4*log(2))/4,a(4)=exp(4*log(1))=16。
求和{k=1..n}τ(6*k)~(15*n*(log(n)+2*gamma-1)+n*(5*log(2)+3*log。
求和{k=1..n}τ(8*k)~(20*n*(log(n)+2*gamma-1)+n*12*log(2))/8,a(8)=exp(12*log。
和{k=1..n}τ(9*k)~(21*n*(log(n)+2*gamma-1)+n*6*log(3))/9,a(9)=exp。
求和{k=1..n}τ(10*k)~(27*n*(log(n)+2*gamma-1)+n*(9*log(2)+3*log。
求和{k=1..n}τ(12*k)~(40*n*(log(n)+2*gamma-1)+n*(20*log(2)+8*log。
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