来自在线整数百科全书的问候语!http://oeis.org/ Search: id:a069184 Showing 1-1 of 1 %I A069184 %S A069184 1,3,4,5,6,12,8,9,13,18,12,20,14,24,24,17,18,39,20,30,32,36,24,36,31, %T A069184 42,40,40,30,72,32,33,48,54,48,65,38,60,56,54,42,96,44,60,78,72,48,68, %U A069184 57,93,72,70,54,120,72,72,80,90,60,120,62,96,104,65,84,144,68,90,96 %N A069184 Sum of divisors d of n such that d or n/d is odd. %C A069184 Might be called UnitaryOrdinarySigma(n): If n=Product p_i^r_i then UOSigma(n)=UnitarySigma(2^r_1)*Sigma(n/2^r_1)=(2^r_1+1)*Product (p_i^(r_i+1)-1)/(p_i-1), p_i is not 2. 6月11日,2005岁,Antti Karttunen,n,a(n)n=1…16384的表%H A069184与除数之和有关的序列的索引条目(p^(e+1)-1)/(p-1)为奇素数p<%f f a069184 G.F.:SUMU{{M*X*M*(1 +x^ M+x^(2×m)-x^(3×m))/(1-x^(4×m)).%F A069184Dirichlet G.:zeta(s)*zeta(s-1)*(2 ^(2-3s)-2 ^(1-2s)-2 ^(1-s)+y)/(1-^ ^(1-s))。%f a069184乘以A(2 ^ e)=2 ^ E+ 1和A(p^ e)=-J.MathARug,Jun 02,2011πF A069184 SuMu{{K=1…n} A(k)~7*π^ 2 *N ^ 2/96。- _Vaclav Kotesovec_, Feb 08 2019 %e A069184 UOSigma(2^4*7^2) = UnitarySigma(2^4)*sigma(7^2) = 17*57 = 969. %p A069184 A069184 := proc(n) local a,f,p,e; a := 1 ; for f in ifactors(n)[2] do p := op(1,f) ; e := op(2,f) ; if p = 2 then a := a*(2^e+1) ; else a := a*(p^(e+1)-1)/(p-1) ; end if; end do; a ; end proc: # _R. J. Mathar_, Jun 02 2011 %t A069184 Table[ Sum[ d*Boole[ OddQ[d] || OddQ[n/d] ], {d, Divisors[n]}], {n, 1, 69}] (* _Jean-François Alcover_, Mar 26 2013 *) %o A069184 (PARI) a(n) = sumdiv(n, d, d*((d % 2) || ((n/d) % 2))); \\ _Michel Marcus_, Apr 10 2014 %o A069184 (PARI) a(n)=my(e=valuation(n,2)); sigma(n>>e) * if(e,2^e+1,1) \\ _Charles R Greathouse IV_, Apr 10 2014 %Y A069184 Cf. A069733, A107749, A092356. %K A069184 mult,nonn %O A069184 1,2 %A A069184 _Vladeta Jovovic_, Apr 10 2002 %E A069184 Edited by _N. J. A. Sloane_, Aug 29 2008 at the suggestion of R. J. Mathar # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE