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
Keywords
Examples
The divisors of 12 which are <= sqrt(12) are 1,2,3, so a(12) = 1^2 + 2^2 + 3^2 = 14.
Links
- Michael De Vlieger, Table of n, a(n) for n = 1..10000
Programs
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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 *) -
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
Formula
G.f.: Sum_{n>=1} n^2*x^(n^2)/(1-x^n). - Joerg Arndt, Jan 30 2011