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A317846 Numerators of rational valued sequence whose Dirichlet convolution with itself yields sequence A051953 (cototient of n) + A063524 (1, 0, 0, 0, ...). 6
1, 1, 1, 7, 1, 7, 1, 25, 11, 11, 1, 43, 1, 15, 13, 363, 1, 71, 1, 67, 17, 23, 1, 139, 19, 27, 61, 91, 1, 57, 1, 1335, 25, 35, 21, 365, 1, 39, 29, 215, 1, 81, 1, 139, 131, 47, 1, 1875, 27, 199, 37, 163, 1, 367, 29, 291, 41, 59, 1, 235, 1, 63, 171, 9923, 33, 129, 1, 211, 49, 137, 1, 1055, 1, 75, 235, 235, 33, 153, 1, 2883, 1363, 83, 1, 335, 41 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

The first negative term is a(420) = -1269.

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) * (A051953(n) - Sum_{d|n, d>1, d<n} f(d) * f(n/d)) for n > 1.

PROG

(PARI)

A317846aux(n) = if(1==n, n, ((n-eulerphi(n))-sumdiv(n, d, if((d>1)&&(d<n), A317846aux(d)*A317846aux(n/d), 0)))/2);

A317846(n) = numerator(A317846aux(n));

(PARI)

\\ Memoized implementation:

memo317846 = Map();

A317846aux(n) = if(1==n, n, if(mapisdefined(memo317846, n), mapget(memo317846, n), my(v = ((n-eulerphi(n))-sumdiv(n, d, if((d>1)&&(d<n), A317846aux(d)*A317846aux(n/d), 0)))/2); mapput(memo317846, n, v); (v)));

CROSSREFS

Cf. A051953, A063524, A046644 (denominators).

Cf. also A317845, A317925.

Sequence in context: A344698 A010688 A176415 * A198219 A198580 A160798

Adjacent sequences:  A317843 A317844 A317845 * A317847 A317848 A317849

KEYWORD

sign,frac

AUTHOR

Antti Karttunen, Aug 12 2018

STATUS

approved

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Last modified July 26 15:49 EDT 2021. Contains 346294 sequences. (Running on oeis4.)