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

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));

Crossrefs

Cf. A003415, A003602.

Cf. also A347954, A347956.

Sequence in context: A021197 A286872 A363514 * A349133 A347131 A350515

Adjacent sequences: A347952 A347953 A347954 * A347956 A347957 A347958

Keyword

nonn

Author

Antti Karttunen, Sep 20 2021

Status

approved