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

Author

Antti Karttunen, Aug 11 2018

Keywords

• nonn
• frac

Links

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

Crossrefs

Cf. A005187, A317927 (numerators).

Cf. also A297111, A300244, A299152, A317932.

Programs

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)&&(dA317927perA317928(d)*A317927perA317928(n/d),0)))/2);
A317928(n) = denominator(A317927perA317928(n));

Formula

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