A347955 - OEIS

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A347955

Dirichlet convolution of A003415 (arithmetic derivative) with A003602 (Kimberling's paraphrases).

0, 1, 1, 5, 1, 8, 1, 17, 8, 11, 1, 32, 1, 14, 13, 49, 1, 44, 1, 47, 16, 20, 1, 100, 13, 23, 44, 62, 1, 81, 1, 129, 22, 29, 19, 156, 1, 32, 25, 151, 1, 106, 1, 92, 86, 38, 1, 276, 18, 92, 31, 107, 1, 206, 25, 202, 34, 47, 1, 301, 1, 50, 111, 321, 28, 156, 1, 137, 40, 151, 1, 460, 1, 59, 120, 152, 28, 181, 1, 423, 206

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OFFSET

1,4

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..16384

FORMULA

a(n) = Sum_{d|n} A003415(n/d) * A003602(d).

PROG

(PARI)

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));

A003602(n) = (1+(n>>valuation(n, 2)))/2;

A347955(n) = sumdiv(n, d, A003415(n/d)*A003602(d));