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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
OFFSET
1,4
COMMENTS
The first negative term is a(360) = -12947.
LINKS
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
KEYWORD
sign,frac
AUTHOR
Antti Karttunen, Aug 12 2018
STATUS
approved