A317938 Numerators of rational valued sequence whose Dirichlet convolution with itself yields sequence A001222 (bigomega n) + A063524 (1, 0, 0, 0, ...).

1, 1, 1, 7, 1, 3, 1, 17, 7, 3, 1, 11, 1, 3, 3, 139, 1, 11, 1, 11, 3, 3, 1, 15, 7, 3, 17, 11, 1, 3, 1, 263, 3, 3, 3, 17, 1, 3, 3, 15, 1, 3, 1, 11, 11, 3, 1, 83, 7, 11, 3, 11, 1, 15, 3, 15, 3, 3, 1, -3, 1, 3, 11, 995, 3, 3, 1, 11, 3, 3, 1, 11, 1, 3, 11, 11, 3, 3, 1, 83, 139, 3, 1, -3, 3, 3, 3, 15, 1, -3, 3, 11, 3, 3, 3, 189, 1, 11, 11, 17, 1, 3, 1, 15, 3

Offset

1,4

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Formula

a(n) = numerator of f(n), where f(1) = 1, f(n) = (1/2) * (A001222(n) - Sum_{d|n, d>1, d<n} f(d) * f(n/d)) for n > 1.

Prog

(PARI)
A317938aux(n) = if(1==n, n, (bigomega(n)-sumdiv(n, d, if((d>1)&&(d<n), A317938aux(d)*A317938aux(n/d), 0)))/2);
A317938(n) = numerator(A317938aux(n));
(PARI)
\\ Memoized implementation:
memo317938 = Map();
A317938aux(n) = if(1==n, n, if(mapisdefined(memo317938, n), mapget(memo317938, n), my(v = (bigomega(n)-sumdiv(n, d, if((d>1)&&(d<n), A317938aux(d)*A317938aux(n/d), 0)))/2); mapput(memo317938, n, v); (v)));

Crossrefs

Cf. A001222, A063524, A046644 (denominators).

Cf. also A317831, A317925, A317933, A317845, A317846, A317937.

Sequence in context: A370112 A200923 A317830 * A317834 A340144 A340141

Adjacent sequences: A317935 A317936 A317937 * A317939 A317940 A317941

Keyword

sign,frac

Author

Antti Karttunen, Aug 12 2018

Status

approved