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A347133
a(n) = Sum_{d|n} A003415(n/d) * A069359(d).
6
0, 0, 0, 1, 0, 2, 0, 6, 1, 2, 0, 16, 0, 2, 2, 24, 0, 19, 0, 20, 2, 2, 0, 72, 1, 2, 9, 24, 0, 40, 0, 80, 2, 2, 2, 111, 0, 2, 2, 96, 0, 48, 0, 32, 25, 2, 0, 256, 1, 29, 2, 36, 0, 117, 2, 120, 2, 2, 0, 244, 0, 2, 29, 240, 2, 64, 0, 44, 2, 56, 0, 446, 0, 2, 31, 48, 2, 72, 0, 352, 54, 2, 0, 308, 2, 2, 2, 168, 0, 304, 2, 56
OFFSET
1,6
COMMENTS
Dirichlet convolution of A003415 (arithmetic derivative) with A069359.
Dirichlet convolution of A001221 (omega, number of distinct prime factors of n) with A347131.
FORMULA
a(n) = Sum_{d|n} A003415(n/d) * A069359(d).
a(n) = Sum_{d|n} A001221(n/d) * A347131(d).
PROG
(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A069359(n) = (n*sumdiv(n, d, isprime(d)/d)); \\ From A069359
A347133(n) = sumdiv(n, d, A003415(n/d)*A069359(d));
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Aug 23 2021
STATUS
approved