A347389 Dirichlet convolution of A003415(n) and A003415(A276086(n)), where A003415(n) is the arithmetic derivative of n, and A276086(n) gives the prime product form of primorial base expansion of n.

0, 1, 1, 5, 1, 11, 1, 22, 11, 29, 1, 48, 1, 17, 34, 76, 1, 84, 1, 160, 22, 137, 1, 172, 31, 61, 88, 130, 1, 404, 1, 456, 142, 725, 40, 411, 1, 297, 66, 900, 1, 1262, 1, 1984, 421, 4001, 1, 1244, 21, 1866, 730, 2382, 1, 6574, 160, 8740, 302, 22157, 1, 1930, 1, 43, 1249, 1530, 84, 2222, 1, 2968, 4006, 568, 1, 1860

Offset

1,4

Links

Antti Karttunen, Table of n, a(n) for n = 1..2309

Index entries for sequences related to primorial base

Formula

a(n) = Sum_{d|n} A003415(n/d) * A327860(d).

Prog

(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A347389(n) = sumdiv(n, d, A003415(n/d) * A003415(A276086(d)));

Crossrefs

Cf. A003415, A276086, A327860.

Cf. also A345000.

Sequence in context: A062967 A245211 A356775 * A330774 A296307 A238554

Adjacent sequences: A347386 A347387 A347388 * A347390 A347391 A347392

Keyword

nonn,base,look

Author

Antti Karttunen, Sep 02 2021

Status

approved