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A294567 a(n) = Sum_{d|n} d^(1 + 2*n/d). 2
1, 9, 28, 97, 126, 588, 344, 2049, 2917, 6174, 1332, 53764, 2198, 52320, 258648, 430081, 4914, 2463429, 6860, 8352582, 15181712, 8560308, 12168, 242240964, 48843751, 134606598, 1167064120, 1651526120, 24390, 14202123408, 29792, 25905102849, 94162701936 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

If p is prime, a(p) = 1 + p^3. - Robert Israel, Nov 03 2017

LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..3143

FORMULA

L.g.f.: -log(Product_{k>=1} (1 - k^2*x^k)) = Sum_{n>=1} a(n)*x^n/n. - Ilya Gutkovskiy, Mar 12 2018

MAPLE

f:= n -> add(d^(1+2*n/d), d=numtheory:-divisors(n)):

map(f, [$1..100]); # Robert Israel, Nov 03 2017

MATHEMATICA

sd[n_] := Module[{d = Divisors[n]}, Total[d^(1 + (2 n)/d)]]; Array[sd, 40] (* Harvey P. Dale, Mar 17 2020 *)

PROG

(PARI) a(n) = sumdiv(n, d, d^(1+2*n/d)); \\ Michel Marcus, Nov 02 2017

CROSSREFS

Column k=2 of A294579.

Cf. A292164.

Sequence in context: A001158 A171215 A296601 * A053819 A294287 A085292

Adjacent sequences:  A294564 A294565 A294566 * A294568 A294569 A294570

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Nov 02 2017

STATUS

approved

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Last modified March 6 07:15 EST 2021. Contains 341842 sequences. (Running on oeis4.)