login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A343574 a(n) = Sum_{d|n} d^d * binomial(d+n/d-1, d). 3
1, 6, 30, 272, 3130, 46794, 823550, 16778544, 387420768, 10000018820, 285311670622, 8916100779324, 302875106592266, 11112006832146486, 437893890380925960, 18446744073860555680, 827240261886336764194, 39346408075300413088392 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..18.

FORMULA

G.f.: Sum_{k >= 1} (k * x)^k/(1 - x^k)^(k+1).

If p is prime, a(p) = p + p^p.

MATHEMATICA

a[n_] := DivisorSum[n, #^#*Binomial[# + n/# - 1, #] &]; Array[a, 20] (* Amiram Eldar, Apr 20 2021 *)

PROG

(PARI) a(n) = sumdiv(n, d, d^d*binomial(d+n/d-1, d));

(PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, (k*x)^k/(1-x^k)^(k+1)))

CROSSREFS

Cf. A081543, A343568, A343573.

Sequence in context: A277073 A052585 A304188 * A051821 A099031 A066108

Adjacent sequences:  A343571 A343572 A343573 * A343575 A343576 A343577

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Apr 20 2021

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 20 23:44 EDT 2021. Contains 345316 sequences. (Running on oeis4.)