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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.
5
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
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. also A345000.
Sequence in context: A062967 A245211 A356775 * A330774 A296307 A238554
KEYWORD
nonn,base,look
AUTHOR
Antti Karttunen, Sep 02 2021
STATUS
approved