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A318498 Denominators of the sequence whose Dirichlet convolution with itself yields A061389, number of (1+phi)-divisors of n. 4
1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 8, 1, 2, 1, 2, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 8, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 8, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 16, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 8, 8, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 8, 1, 2, 2, 4, 1, 1, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

The sequence seems to give the denominators of a few other similarly constructed rational valued sequences obtained as "Dirichlet Square Roots" (of possibly A092520 and A293443).

LINKS

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

FORMULA

a(n) = denominator of f(n), where f(1) = 1, f(n) = (1/2) * (A061389(n) - Sum_{d|n, d>1, d<n} f(d) * f(n/d)) for n > 1.

a(n) = 2^A318499(n).

PROG

(PARI)

up_to = 65537;

A061389(n) = factorback(apply(e -> (1+eulerphi(e)), factor(n)[, 2]));

DirSqrt(v) = {my(n=#v, u=vector(n)); u[1]=1; for(n=2, n, u[n]=(v[n]/v[1] - sumdiv(n, d, if(d>1&&d<n, u[d]*u[n/d], 0)))/2); u}; \\ From A317937.

v318497_98 = DirSqrt(vector(up_to, n, A061389(n)));

A318497(n) = numerator(v318497_98[n]);

A318498(n) = denominator(v318497_98[n]);

CROSSREFS

Cf. A061389, A318497 (numerators), A318499.

Cf. also A299150, A046644.

Sequence in context: A056624 A193348 A263723 * A093997 A157196 A300410

Adjacent sequences:  A318495 A318496 A318497 * A318499 A318500 A318501

KEYWORD

nonn,frac

AUTHOR

Antti Karttunen, Aug 30 2018

STATUS

approved

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Last modified October 22 07:29 EDT 2019. Contains 328315 sequences. (Running on oeis4.)