|
| |
|
|
A344080
|
|
a(n) = Sum_{d|n} tau(d)^n, where tau(n) is the number of divisors of n.
|
|
3
|
|
|
|
1, 5, 9, 98, 33, 4225, 129, 72354, 20196, 1050625, 2049, 2194099186, 8193, 268468225, 1073807361, 156925970179, 131073, 101629064089930, 524289, 3657261440572306, 4398050705409, 17592194433025, 8388609, 4727105427440383342818, 847322163876, 4503599761588225
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,2
|
|
|
LINKS
|
Seiichi Manyama, Table of n, a(n) for n = 1..719
|
|
|
FORMULA
|
G.f.: Sum_{k >= 1} (tau(k) * x)^k/(1 - (tau(k) * x)^k).
If p is prime, a(p) = 1 + 2^p.
|
|
|
MATHEMATICA
|
a[n_] := DivisorSum[n, DivisorSigma[0, #]^n &]; Array[a, 26] (* Amiram Eldar, May 09 2021 *)
|
|
|
PROG
|
(PARI) a(n) = sumdiv(n, d, numdiv(d)^n);
(PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, (numdiv(k)*x)^k/(1-(numdiv(k)*x)^k)))
|
|
|
CROSSREFS
|
Cf. A007425, A062367, A097988, A279789, A344060, A344081.
Sequence in context: A344081 A171812 A221741 * A098097 A279707 A329002
Adjacent sequences: A344077 A344078 A344079 * A344081 A344082 A344083
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
Seiichi Manyama, May 09 2021
|
|
|
STATUS
|
approved
|
| |
|
|
