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A318650 Numerators of the sequence whose Dirichlet convolution with itself yields A057521, the powerful part of n. 1
1, 1, 1, 15, 1, 1, 1, 49, 35, 1, 1, 15, 1, 1, 1, 603, 1, 35, 1, 15, 1, 1, 1, 49, 99, 1, 181, 15, 1, 1, 1, 2023, 1, 1, 1, 525, 1, 1, 1, 49, 1, 1, 1, 15, 35, 1, 1, 603, 195, 99, 1, 15, 1, 181, 1, 49, 1, 1, 1, 15, 1, 1, 35, 14875, 1, 1, 1, 15, 1, 1, 1, 1715, 1, 1, 99, 15, 1, 1, 1, 603, 3235, 1, 1, 15, 1, 1, 1, 49, 1, 35, 1, 15, 1, 1, 1, 2023, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Multiplicative because A046644 and A057521 are.

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) * (A057521(n) - Sum_{d|n, d>1, d<n} f(d) * f(n/d)) for n > 1.

PROG

(PARI)

up_to = 65537;

A057521(n) = { my(f=factor(n)); prod(i=1, #f~, if(f[i, 2]>1, f[i, 1]^f[i, 2], 1)); }; \\ From A057521

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};

v318650_aux = DirSqrt(vector(up_to, n, A057521(n)));

A318650(n) = numerator(v318650_aux[n]);

CROSSREFS

Cf. A057521, A046644 (denominators).

Cf. also A317935, A318511, A318649.

Sequence in context: A015908 A040228 A040229 * A281571 A040227 A040226

Adjacent sequences:  A318647 A318648 A318649 * A318651 A318652 A318653

KEYWORD

nonn,frac,mult

AUTHOR

Antti Karttunen, Aug 31 2018

STATUS

approved

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Last modified March 20 20:14 EDT 2019. Contains 321352 sequences. (Running on oeis4.)