A069292 Sum of square roots of square divisors of n <= sqrt(n).

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 4, 1, 1, 3, 1, 1, 1, 3, 1, 4, 1, 3, 1, 1, 1, 3, 1, 1, 4, 3, 1, 1, 1, 3, 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. A035316, A046951, A000188, A069290, A069291, A069293.

Programs

Mathematica

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

PARI

A069292(n) = { my(r="NA"); sumdiv(n, d, (issquare(d,&r)&&((d^2)<=n))*r); } \\ Antti Karttunen, Nov 20 2017

Formula

G.f.: Sum_{k>=1} k * x^(k^4) / (1 - x^(k^2)). - Ilya Gutkovskiy, Aug 19 2021

Extensions

More terms from Antti Karttunen, Nov 20 2017