A317835 - OEIS

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A317835

Numerators of rational valued sequence whose Dirichlet convolution with itself yields sequence A003415 (arithmetic derivative of n) + A063524 (1, 0, 0, 0, ...).

1, 1, 1, 15, 1, 9, 1, 81, 23, 13, 1, 95, 1, 17, 15, 1499, 1, 127, 1, 151, 19, 25, 1, 393, 39, 29, 193, 207, 1, 87, 1, 6311, 27, 37, 23, 969, 1, 41, 31, 661, 1, 119, 1, 319, 259, 49, 1, 5499, 55, 295, 39, 375, 1, 769, 31, 929, 43, 61, 1, 593, 1, 65, 347, 50075, 35, 183, 1, 487, 51, 183, 1, 2751, 1, 77, 371, 543, 35, 215, 1, 9643, 5611, 85, 1

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OFFSET

1,4

COMMENTS

The first negative term is a(240) = -5067.

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) * (A003415(n) - Sum_{d|n, d>1, d<n} f(d) * f(n/d)) for n > 1.

PROG

(PARI)

A003415(n) = {my(fac); if(n<1, 0, fac=factor(n); sum(i=1, matsize(fac)[1], n*fac[i, 2]/fac[i, 1]))}; \\ From A003415