A396262 - OEIS

A396262

a(n) = Sum_{d|n, d < sqrt(n)} (-1)^(n/d) * d^2.

0, 1, -1, 1, -1, -3, -1, 5, -1, -3, -1, 14, -1, -3, -10, 5, -1, 6, -1, -11, -10, -3, -1, 30, -1, -3, -10, -11, -1, 31, -1, 21, -10, -3, -26, -2, -1, -3, -10, 46, -1, -30, -1, -11, -35, -3, -1, 66, -1, 22, -10, -11, -1, -30, -26, 70, -10, -3, -1, 59, -1, -3, -59, 21, -26, -30, -1, -11, -10, 71

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OFFSET

1,6

LINKS

Table of n, a(n) for n=1..70.

FORMULA

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

MATHEMATICA

Table[DivisorSum[n, (-1)^(n/#) #^2 &, # < Sqrt@ n &], {n, 1, 70}]

(* Alternative: *)

nmax = 70; CoefficientList[Series[Sum[(-1)^(k + 1) k^2 x^(k (k + 1))/(1 + x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Rest

CROSSREFS