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A318671 Numerators of the sequence whose Dirichlet convolution with itself yields A049599, number of (1+e)-divisors of n. 2
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -3 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,64

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) * (A049599(n) - Sum_{d|n, d>1, d<n} f(d) * f(n/d)) for n > 1.

PROG

(PARI)

up_to = (2^16)+1;

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};

A049599(n) = factorback(apply(e -> (1+numdiv(e)), factor(n)[, 2]));

v318671_72 = DirSqrt(vector(up_to, n, A049599(n)));

A318671(n) = numerator(v318671_72[n]);

CROSSREFS

Cf. A049599, A318672 (denominators).

Sequence in context: A216792 A260237 A118135 * A109014 A268357 A321804

Adjacent sequences:  A318668 A318669 A318670 * A318672 A318673 A318674

KEYWORD

sign,frac

AUTHOR

Antti Karttunen, Sep 03 2018

STATUS

approved

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Last modified April 23 07:51 EDT 2019. Contains 322381 sequences. (Running on oeis4.)