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A294567 a(n) = Sum_{d|n} d^(1 + 2*n/d). 2

%I

%S 1,9,28,97,126,588,344,2049,2917,6174,1332,53764,2198,52320,258648,

%T 430081,4914,2463429,6860,8352582,15181712,8560308,12168,242240964,

%U 48843751,134606598,1167064120,1651526120,24390,14202123408,29792,25905102849,94162701936

%N a(n) = Sum_{d|n} d^(1 + 2*n/d).

%C If p is prime, a(p) = 1 + p^3. - _Robert Israel_, Nov 03 2017

%H Seiichi Manyama, <a href="/A294567/b294567.txt">Table of n, a(n) for n = 1..3143</a>

%F 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

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

%p map(f, [$1..100]); # _Robert Israel_, Nov 03 2017

%o (PARI) a(n) = sumdiv(n, d, d^(1+2*n/d)); \\ _Michel Marcus_, Nov 02 2017

%Y Column k=2 of A294579.

%Y Cf. A292164.

%K nonn

%O 1,2

%A _Seiichi Manyama_, Nov 02 2017

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Last modified January 25 03:49 EST 2020. Contains 331241 sequences. (Running on oeis4.)