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A317832
Denominators of rational valued sequence f whose Dirichlet convolution with itself yields A000203 (sigma, the sum of divisors).
5
1, 2, 1, 8, 1, 1, 1, 16, 2, 2, 1, 4, 1, 1, 1, 128, 1, 4, 1, 8, 1, 1, 1, 8, 1, 2, 1, 2, 1, 1, 1, 256, 1, 2, 1, 16, 1, 1, 1, 16, 1, 1, 1, 4, 2, 1, 1, 64, 2, 2, 1, 8, 1, 2, 1, 4, 1, 2, 1, 4, 1, 1, 1, 1024, 1, 1, 1, 8, 1, 1, 1, 32, 1, 2, 1, 4, 1, 1, 1, 128, 8, 2, 1, 1, 1, 1, 1, 8, 1, 4, 1, 2, 1, 1, 1, 128, 1, 4, 1, 8, 1, 1, 1, 16, 1
OFFSET
1,2
FORMULA
a(n) = denominator of f(n), where f(1) = 1, f(n) = (1/2) * (A000203(n) - Sum_{d|n, d>1, d<n} f(d) * f(n/d)) for n > 1.
PROG
(PARI)
A317831perA317832(n) = if(1==n, n, (sigma(n)-sumdiv(n, d, if((d>1)&&(d<n), A317831perA317832(d)*A317831perA317832(n/d), 0)))/2);
A317832(n) = denominator(A317831perA317832(n));
CROSSREFS
Cf. A317831 (gives the numerators).
Cf. also A000203, A299152.
Sequence in context: A330187 A323690 A152901 * A317928 A011327 A318454
KEYWORD
nonn,frac
AUTHOR
Antti Karttunen, Aug 10 2018
STATUS
approved