A095118 a(n) is the sum of the squares of the divisors of n which are <= sqrt(n).

1, 1, 1, 5, 1, 5, 1, 5, 10, 5, 1, 14, 1, 5, 10, 21, 1, 14, 1, 21, 10, 5, 1, 30, 26, 5, 10, 21, 1, 39, 1, 21, 10, 5, 26, 66, 1, 5, 10, 46, 1, 50, 1, 21, 35, 5, 1, 66, 50, 30, 10, 21, 1, 50, 26, 70, 10, 5, 1, 91, 1, 5, 59, 85, 26, 50, 1, 21, 10, 79, 1, 130, 1, 5, 35, 21, 50, 50, 1, 110, 91

Offset

1,4

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Formula

G.f.: Sum_{n>=1} n^2*x^(n^2)/(1-x^n). - Joerg Arndt, Jan 30 2011

Example

The divisors of 12 which are <= sqrt(12) are 1,2,3, so a(12) = 1^2 + 2^2 + 3^2 = 14.

Mathematica

a[n_]:=Plus@@(Select[Divisors[n], #^2<=n&]^2)
(* Second program: *)
Table[DivisorSum[n, #^2 &, # <= Sqrt@ n &], {n, 81}] (* Michael De Vlieger, Dec 14 2017 *)

Prog

(PARI) N=100; x='x+O('x^N); Vec( sum(n=1, N, n^2*x^(n^2)/(1-x^n) ) ) \\ Joerg Arndt, Jan 02 2017
(PARI) a(n) = my(rn = sqrt(n)); sumdiv(n, d, d^2*(d<=rn)); \\ Michel Marcus, Jan 02 2017

Crossrefs

Cf. A095119, A066839.

Sequence in context: A083528 A056957 A224834 * A251417 A100947 A096940

Adjacent sequences: A095115 A095116 A095117 * A095119 A095120 A095121

Keyword

nonn

Author

Dean Hickerson, following a suggestion of Leroy Quet, May 28 2004

Status

approved