A343544 a(n) = n * Sum_{d|n} binomial(d+2,3)/d.

1, 6, 13, 32, 40, 94, 91, 184, 204, 320, 297, 612, 468, 770, 850, 1184, 986, 1752, 1349, 2280, 2114, 2662, 2323, 4184, 3125, 4264, 4266, 5740, 4524, 7660, 5487, 8352, 7546, 9180, 8470, 13212, 9176, 12654, 12194, 16640, 12382, 19628, 14233, 20724, 19590, 22034, 18471, 30416, 21462

Offset

1,2

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

G.f.: Sum_{k>=1} k * x^k/(1 - x^k)^4 = Sum_{k>=1} binomial(k+2,3) * x^k/(1 - x^k)^2.

Maple

f:= n -> n/6*add((d+1)*(d+2), d=numtheory:-divisors(n)):
map(f, [$1..100]); # Robert Israel, Apr 26 2021

Mathematica

a[n_] := n * DivisorSum[n, Binomial[# + 2, 3]/# &]; Array[a, 50] (* Amiram Eldar, Apr 25 2021 *)

Prog

(PARI) a(n) = n*sumdiv(n, d, binomial(d+2, 3)/d);
(PARI) my(N=66, x='x+O('x^N)); Vec(sum(k=1, N, binomial(k+2, 3)*x^k/(1-x^k)^2))

Crossrefs

Cf. A000203, A038040, A059358, A309731, A343545, A343546, A343547.

Sequence in context: A101622 A256871 A192304 * A147330 A042607 A048693

Adjacent sequences: A343541 A343542 A343543 * A343545 A343546 A343547

Keyword

nonn

Author

Seiichi Manyama, Apr 19 2021

Status

approved