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A317938 Numerators of rational valued sequence whose Dirichlet convolution with itself yields sequence A001222 (bigomega n) + A063524 (1, 0, 0, 0, ...). 4
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 (list; graph; refs; listen; history; text; internal format)
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: A130875 A200923 A317830 * A317834 A340144 A340141

Adjacent sequences:  A317935 A317936 A317937 * A317939 A317940 A317941

KEYWORD

sign,frac

AUTHOR

Antti Karttunen, Aug 12 2018

STATUS

approved

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Last modified June 16 14:16 EDT 2021. Contains 345057 sequences. (Running on oeis4.)