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

1,4

Comments

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

Links

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

Formula

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

Prog

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

Crossrefs

Cf. A001065, A063524, A046644 (denominators).

Cf. also A317831, A317846.

Sequence in context: A266327 A274216 A280524 * A278599 A281036 A205321

Adjacent sequences: A317842 A317843 A317844 * A317846 A317847 A317848

Keyword

sign,frac

Author

Antti Karttunen, Aug 12 2018

Status

approved