来自在线整数百科全书的问候语!http://oeis.org/ Search: id:a070824 Showing 1-1 of 1 %I A070824 %S A070824 0,0,0,1,0,2,0,2,1,2,0,4,0,2,2,3,0,4,0,4,2,2,0,6,1,2,2,4,0,6,0,4,2,2, %T A070824 2,7,0,2,2,6,0,6,0,4,4,2,0,8,1,4,2,4,0,6,2,6,2,2,0,10,0,2,4,5,2,6,0,4, %U A070824 2,6,0,10,0,2,4,4,2,6,0,8,3,2,0,10,2,2 %N A070824 Number of divisors of n which are > 1 and < n (nontrivial divisors). %C A070824 These are sometimes called the proper divisors (see A032741 for the usual meaning of that term) %C A070824 a(n) = number of ordered factorizations of n into two factors, n = 2,3,... 如果n具有素数分解n=乘积p^ e(j),j=1…r,则向量(e(1),…,e(r))的合成数等于n(安德鲁斯,1998,59)的有序分解数给出了(e(1),…,(r))m个数的公式,它等于n的有序m分解的数f(n,m),但m=2,公式减少到f(n,2)=d(n)-2=a(n)。-奥古斯丁O.Munaigi],3月31日2005πC A070824 A(n)=0,当且仅当n为1或素数时。-n Jon Pyryv,NOV 08 2008 2008 %C A070824为n>2:第0行三角形A051778的零点数。-12 ReHand HuZunkeleLez,DEC 03 2014 2014 %C A070824 A(n)=n的最大数目和最小部分恰好出现一次,它们的差为2。例如:A(12)=4,因为我们有[7],[5],[4],[3],[4,3,3,2]和[3,2,2,2,1]。一般来说,如果D是n的非平凡除数,则[D+1,{d}^(n/d2),d1]是n的指定类型的划分。-德意志03,2015,安德鲁斯,G. E.,分裂理论,Addison Wesley,阅读1976;再版,剑桥大学出版社,剑桥,1984, 1998。n,a(n)n=1…10000的表%H A070824 Arnold Knopfmacher和Michael Mays,整数的有序与无序分解,Mathematica杂志,第10卷(1).0%F A070824A(n)=a00 00 05(n)- 2,n>=2(带除数函数D(n)=a00 00 05(n)).% f f a070824 a(n)=d(n)-2,其中d(n)是除数函数。例如A(12)=4,因为12有4个有序因子分解成两个因子:2×6, 6×2, 3×4, 4×3。-奥古斯丁O.Munaigi],3月31日2005πF A070824 G.F.:SuMux{K=2 ..无穷大X^(2K)/(1-x^ k)。-Yon Jon Pryrv,NOV 08 2008πF A070824 Dirichlet生成函数:(ζ(s)- 1)^ 2 [Y-Mats Grimvik] 5月25日2013 ] [%e] A070824 A(12)=4,与非平凡除数2,3,4,6 ..% E E A070824 A(24)=6=卡({{2,12},{3,8},{4},6},{6},4},{8},3},{12,2}。- _Peter Luschny_, Nov 14 2011 %p A070824 0, seq(numtheory[tau](n)-2,n=2..100); # _Augustine O. Munagi_, Mar 31 2005 %t A070824 Join[{0},Rest[DivisorSigma[0,Range[90]]-2]] (* _Harvey P. Dale_, Jun 23 2012 *) %t A070824 a[ n_] := SeriesCoefficient[ Sum[x^(2 k)/(1 - x^k), {k, 2, n/2}], {x, 0, n}]; (* _Michael Somos_, Jun 24 2019 *) %o A070824 (Haskell) %o A070824 a070824 n = if n == 1 then 0 else length $ tail $ a027751_row n %o A070824 -- _Reinhard Zumkeller_, Dec 03 2014 %o A070824 (PARI) {a(n) = if( n<1, 0, my(v = vector(n, i, i>1)); dirmul(v, v)[n])}; /* _Michael Somos_, Jun 24 2019 */ %Y A070824 Cf. A000005, A074206, A032741, A200213. %Y A070824 Cf. First column in the matrix power A175992^2 %Y A070824 Row sums of A175992 starting from the second column. %Y A070824 Cf. A027751, A051778. %Y A070824 Column k=2 of A251683. %K A070824 nonn,easy %O A070824 1,6 %A A070824 _Wolfdieter Lang_, May 08 2002 %E A070824 a(1)=0 added by _Peter Luschny_, Nov 14 2011 # Content is available under The OEIS End-User License协议:HTTP//OEIS.Org/许可证