login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A027848 a(n) = Sum_{ d|n } sigma(n/d)*d^4. 8
1, 19, 85, 311, 631, 1615, 2409, 4991, 6898, 11989, 14653, 26435, 28575, 45771, 53635, 79887, 83539, 131062, 130341, 196241, 204765, 278407, 279865, 424235, 394406, 542925, 558778, 749199, 707311, 1019065, 923553, 1278255, 1245505, 1587241, 1520079, 2145278, 1874199, 2476479, 2428875, 3149321, 2825803, 3890535, 3418845, 4557083, 4352638, 5317435 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
FORMULA
Dirichlet g.f.: zeta(x-1)*zeta(x-4).
Multiplicative with a(p^e) = (p^(4e+7) - (p^3+p^2+p+1)*p^(e+1) + p^2+p+1)/(p^7 - (p^3+p^2+p+1)*p + p^2+p+1). - Mitch Harris, Jun 27 2005
L.g.f.: -log(Product_{k>=1} (1 - x^k)^sigma_3(k)) = Sum_{n>=1} a(n)*x^n/n. - Ilya Gutkovskiy, May 23 2018
Sum_{k=1..n} a(k) ~ Pi^4 * n^5 / 450. - Vaclav Kotesovec, Feb 16 2020
MATHEMATICA
f[p_, e_] := (1 + p + p^2 - p^(e+1) - p^(e+2) - p^(e+3) - p^(e+4) + p^(4*e+7))/(1 - p^3 - p^4 + p^7); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 50] (* Amiram Eldar, Oct 03 2023 *)
PROG
(PARI)N=66; x='x+O('x^N); /* that many terms */
c=sum(j=1, N, j*x^j);
t=log(1/prod(j=1, N, eta(x^(j))^(j^3)));
Vec(serconvol(t, c)) /* show terms */
/* Joerg Arndt, May 03 2008 */
CROSSREFS
Sequence in context: A358932 A039609 A063496 * A183623 A039454 A142089
KEYWORD
nonn,easy,mult
AUTHOR
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 16:12 EDT 2024. Contains 371254 sequences. (Running on oeis4.)