A317846 Numerators of rational valued sequence whose Dirichlet convolution with itself yields sequence A051953 (cototient of n) + A063524 (1, 0, 0, 0, ...).

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

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: A176415 A356948 A363150 * A198219 A198580 A160798

Adjacent sequences: A317843 A317844 A317845 * A317847 A317848 A317849

Keyword

sign,frac

Author

Antti Karttunen, Aug 12 2018

Status

approved