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A317940 Numerators of sequence whose Dirichlet convolution with itself yields A046644. 5
1, 1, 1, 7, 1, 1, 1, 9, 7, 1, 1, 7, 1, 1, 1, 427, 1, 7, 1, 7, 1, 1, 1, 9, 7, 1, 9, 7, 1, 1, 1, 471, 1, 1, 1, 49, 1, 1, 1, 9, 1, 1, 1, 7, 7, 1, 1, 427, 7, 7, 1, 7, 1, 9, 1, 9, 1, 1, 1, 7, 1, 1, 7, 4099, 1, 1, 1, 7, 1, 1, 1, 63, 1, 1, 7, 7, 1, 1, 1, 427, 427, 1, 1, 7, 1, 1, 1, 9, 1, 7, 1, 7, 1, 1, 1, 471, 1, 7, 7, 49, 1, 1, 1, 9, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Multiplicative because A046644 is.

No negative terms among the first 2^20 terms. Is the sequence nonnegative?

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) * (A046644(n) - Sum_{d|n, d>1, d<n} f(d) * f(n/d)) for n > 1.

PROG

(PARI)

up_to = 65537;

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.

A005187(n) = { my(s=n); while(n>>=1, s+=n); s; };

A046644(n) = factorback(apply(e -> 2^A005187(e), factor(n)[, 2]));

v317940aux = DirSqrt(vector(up_to, n, A046644(n)));

A317940(n) = numerator(v317940aux[n]);

CROSSREFS

Cf. A005187, A046644, A317934 (denominators), A317941.

Sequence in context: A344696 A336457 A271498 * A318674 A284118 A165725

Adjacent sequences:  A317937 A317938 A317939 * A317941 A317942 A317943

KEYWORD

nonn,frac,mult

AUTHOR

Antti Karttunen, Aug 14 2018

STATUS

approved

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Last modified July 25 03:36 EDT 2021. Contains 346282 sequences. (Running on oeis4.)