A317845 Numerators of rational valued sequence whose Dirichlet convolution with itself yields sequence A001065 (sum of proper divisors) + A063524 (1, 0, 0, 0, ...).

1, 1, 1, 11, 1, 11, 1, 45, 15, 15, 1, 95, 1, 19, 17, 659, 1, 131, 1, 135, 21, 27, 1, 315, 23, 31, 89, 175, 1, 125, 1, 2319, 29, 39, 25, 901, 1, 43, 33, 455, 1, 165, 1, 255, 215, 51, 1, 3739, 31, 291, 41, 295, 1, 671, 33, 595, 45, 63, 1, 731, 1, 67, 271, 16319, 37, 245, 1, 375, 53, 237, 1, 2135, 1, 79, 335, 415, 37, 285, 1, 5419, 1979, 87, 1

Offset: 1

Author

Antti Karttunen, Aug 12 2018

Keywords

• sign
• frac

Comments

The first negative term is a(360) = -12947.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A001065, A063524, A046644 (denominators).

Cf. also A317831, A317846.

Programs

PARI

A317845aux(n) = if(1==n,n,((sigma(n)-n)-sumdiv(n,d,if((d>1)&&(dA317845aux(d)*A317845aux(n/d),0)))/2);
A317845(n) = numerator(A317845aux(n));

Formula

a(n) = numerator of f(n), where f(1) = 1, f(n) = (1/2) * (A001065(n) - Sum_{d|n, d>1, d 1.