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A317830 Numerators of rational valued sequence whose Dirichlet convolution with itself yields A175851, the ordinal transform of the nextprime function, A151800. 6
1, 1, 1, 7, 1, 3, 1, 9, 11, 7, 1, 3, 1, 3, 5, 171, 1, -1, 1, -5, 5, 7, 1, -1, 11, 7, 29, 35, 1, -7, 1, -41, 5, 7, 9, 93, 1, 3, 5, 11, 1, -3, 1, -5, 3, 7, 1, -61, 11, 7, 9, 27, 1, -29, 5, -1, 9, 11, 1, -29, 1, 3, 3, 771, 9, 9, 1, -5, 5, -3, 1, -73, 1, 3, 3, 19, 9, 9, 1, -141, -45, 7, 1, -53, 5, 7, 9, 43, 1, -63, 5, 11, 9, 11, 13, 1597, 1 (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) * (A175851(n) - Sum_{d|n, d>1, d<n} f(d) * f(n/d)) for n > 1.

PROG

(PARI)

A175851(n) = if(1==n, n, 1 + n - precprime(n));

A317830aux(n) = if(1==n, n, (A175851(n)-sumdiv(n, d, if((d>1)&&(d<n), A317830aux(d)*A317830aux(n/d), 0)))/2);

A317830(n) = numerator(A317830aux(n));

(PARI)

\\ Memoized implementation:

memo317830 = Map();

A317830aux(n) = if(1==n, n, if(mapisdefined(memo317830, n), mapget(memo317830, n), my(v = (A175851(n)-sumdiv(n, d, if((d>1)&&(d<n), A317830aux(d)*A317830aux(n/d), 0)))/2); mapput(memo317830, n, v); (v)));

CROSSREFS

Cf. A151800, A175851, A046644 (denominators).

Cf. also A305791, A305805, A305806, A317833, A317834, A317847.

Sequence in context: A239807 A130875 A200923 * A317938 A317834 A340144

Adjacent sequences:  A317827 A317828 A317829 * A317831 A317832 A317833

KEYWORD

sign,frac

AUTHOR

Antti Karttunen, Aug 12 2018

STATUS

approved

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Last modified June 24 10:36 EDT 2021. Contains 345416 sequences. (Running on oeis4.)