A069293 Sum of square divisors of n <= sqrt(n).

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 5, 1, 1, 1, 5, 1, 1, 1, 5, 1, 1, 1, 5, 1, 1, 1, 5, 1, 1, 1, 5, 1, 1, 1, 5, 1, 1, 1, 5, 1, 1, 1, 5, 1, 1, 1, 5, 1, 1, 1, 5, 1, 1, 1, 5, 1, 1, 1, 5, 1, 1, 1, 5, 1, 1, 1, 5, 1, 1, 1, 5, 10, 1, 1, 5, 1, 1, 1, 5, 1, 10, 1, 5, 1, 1, 1, 5, 1, 1, 10, 5, 1, 1, 1, 5, 1

Offset: 1

Author

Reinhard Zumkeller, Mar 14 2002

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Index entries for sequences related to sums of divisors

Crossrefs

Cf. A000188, A035316, A046951, A069290, A069291, A069292.

Programs

Mathematica

Table[DivisorSum[n, # &, And[IntegerQ@ Sqrt@ #, # <= Sqrt@ n] &], {n, 105}] (* Michael De Vlieger, Nov 20 2017 *)

PARI

A069293(n) = sumdiv(n, d, (issquare(d)&&((d^2)<=n))*d); \\ Antti Karttunen, Nov 20 2017

Formula

G.f.: Sum_{k>=1} k^2 * x^(k^4) / (1 - x^(k^2)). - Ilya Gutkovskiy, Apr 04 2020

Extensions

More terms from Antti Karttunen, Nov 20 2017