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A317845 Numerators of rational valued sequence whose Dirichlet convolution with itself yields sequence A001065 (sum of proper divisors) + A063524 (1, 0, 0, 0, ...). 5
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 28 10:29 EDT 2021. Contains 346326 sequences. (Running on oeis4.)