|
|
A034678
|
|
Sum of fourth powers of unitary divisors.
|
|
3
|
|
|
1, 17, 82, 257, 626, 1394, 2402, 4097, 6562, 10642, 14642, 21074, 28562, 40834, 51332, 65537, 83522, 111554, 130322, 160882, 196964, 248914, 279842, 335954, 390626, 485554, 531442, 617314, 707282, 872644, 923522, 1048577, 1200644
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
LINKS
|
|
|
FORMULA
|
Dirichlet g.f.: zeta(s)*zeta(s-4)/zeta(2*s-4). - R. J. Mathar, Mar 04 2011
If n = Product (p_j^k_j) then a(n) = Product (1 + p_j^(4*k_j)). - Ilya Gutkovskiy, Nov 04 2018
|
|
MATHEMATICA
|
Table[Total[Select[Divisors[n], CoprimeQ[#, n/#] &]^4], {n, 1, 50}] (* Vaclav Kotesovec, Feb 01 2019 *)
a[1] = 1; a[n_] := Times @@ (1 + First[#]^(4*Last[#]) & /@ FactorInteger[n]); s = Array[a, 50] (* Amiram Eldar, Aug 10 2019 *)
|
|
PROG
|
(PARI) A000012=direuler(p=2, 119, 1/(1-X)) ;
A000583=direuler(p=2, 119, 1/(1-p^4*X)) ;
A000290x=direuler(p=2, 119, 1-p^4*X^2) ;
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,mult
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|