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A318324 Denominators of rational valued sequence whose Dirichlet convolution with itself yields A046523, smallest number with same prime signature as n. 2
1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 8, 1, 2, 1, 2, 1, 1, 1, 1, 2, 1, 2, 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, 1, 1, 1, 2, 16, 1, 1, 1, 2, 1, 1, 1, 4, 1, 1, 2, 2, 1, 1, 1, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 4, 1, 2, 2, 4, 1, 1, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

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) * (A046523(n) - Sum_{d|n, d>1, d<n} f(d) * f(n/d)) for n > 1.

PROG

(PARI)

up_to = 16384;

A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523

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.

v318323_24 = DirSqrt(vector(up_to, n, A046523(n)));

A318324(n) = denominator(v318323_24[n]);

CROSSREFS

Cf. A046523, A318323 (numerators).

Sequence in context: A347437 A255231 A294874 * A317934 A279848 A001826

Adjacent sequences:  A318321 A318322 A318323 * A318325 A318326 A318327

KEYWORD

nonn,frac

AUTHOR

Antti Karttunen, Aug 24 2018

STATUS

approved

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Last modified September 28 09:32 EDT 2021. Contains 347714 sequences. (Running on oeis4.)