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A318317 Numerators of rational valued sequence whose Dirichlet convolution with itself yields A173557. 3
1, 1, 1, 3, 2, 1, 3, 5, 1, 1, 5, 3, 6, 3, 2, 35, 8, 1, 9, 3, 3, 5, 11, 5, 0, 3, 1, 9, 14, 1, 15, 63, 5, 4, 6, 3, 18, 9, 6, 5, 20, 3, 21, 15, 1, 11, 23, 35, -3, 0, 8, 9, 26, 1, 10, 15, 9, 7, 29, 3, 30, 15, 3, 231, 12, 5, 33, 3, 11, 3, 35, 5, 36, 9, 0, 27, 15, 3, 39, 35, 3, 10, 41, 9, 16, 21, 14, 25, 44, 1, 18, 33, 15, 23, 18, 63, 48, -3, 5, 0, 50, 4, 51, 15, 6 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

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) * (A173557(n) - Sum_{d|n, d>1, d<n} f(d) * f(n/d)) for n > 1.

PROG

(PARI)

up_to = 16384;

A173557(n) = my(f=factor(n)[, 1]); prod(k=1, #f, f[k]-1); \\ From A173557

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.

v318317_18 = DirSqrt(vector(up_to, n, A173557(n)));

A318317(n) = numerator(v318317_18[n]);

CROSSREFS

Cf. A173557, A318318 (denominators).

Cf. also A317925, A317935.

Sequence in context: A081248 A214636 A318582 * A129690 A156665 A215415

Adjacent sequences:  A318314 A318315 A318316 * A318318 A318319 A318320

KEYWORD

sign,frac

AUTHOR

Antti Karttunen, Aug 24 2018

STATUS

approved

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Last modified May 25 01:59 EDT 2019. Contains 323534 sequences. (Running on oeis4.)