A317928 Denominators of rational valued sequence whose Dirichlet convolution with itself yields A005187.

1, 2, 1, 8, 1, 1, 2, 16, 1, 1, 2, 4, 2, 4, 1, 128, 1, 1, 2, 1, 2, 4, 1, 2, 2, 4, 1, 16, 1, 2, 2, 256, 1, 1, 2, 4, 2, 4, 1, 8, 2, 4, 1, 16, 1, 2, 2, 64, 8, 4, 1, 16, 1, 2, 2, 32, 1, 2, 2, 8, 2, 4, 1, 1024, 1, 1, 2, 2, 2, 4, 1, 1, 2, 4, 1, 16, 4, 2, 2, 32, 2, 4, 1, 16, 1, 2, 2, 32, 1, 2, 4, 8, 2, 4, 1, 64, 2, 16, 1, 16, 1, 2, 2, 32, 2

Offset

1,2

Links

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

Formula

a(n) = denominator of f(n), where f(1) = 1, f(n) = (1/2) * (A005187(n) - Sum_{d|n, d>1, d<n} f(d) * f(n/d)) for n > 1.

Prog

(PARI)6
A005187(n) = { my(s=n); while(n>>=1, s+=n); s; };
A317927perA317928(n) = if(1==n, n, (A005187(n)-sumdiv(n, d, if((d>1)&&(d<n), A317927perA317928(d)*A317927perA317928(n/d), 0)))/2);
A317928(n) = denominator(A317927perA317928(n));

Crossrefs

Cf. A005187, A317927 (numerators).

Cf. also A297111, A300244, A299152, A317932.

Sequence in context: A323690 A152901 A317832 * A011327 A318454 A317926

Adjacent sequences: A317925 A317926 A317927 * A317929 A317930 A317931

Keyword

nonn,frac

Author

Antti Karttunen, Aug 11 2018

Status

approved