A317832 Denominators of rational valued sequence f whose Dirichlet convolution with itself yields A000203 (sigma, the sum of divisors).

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

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Index entries for sequences related to sigma(n)

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

Adjacent sequences: A317829 A317830 A317831 * A317833 A317834 A317835

Keyword

nonn,frac

Author

Antti Karttunen, Aug 10 2018

Status

approved