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A349380
Dirichlet convolution of A003415 (arithmetic derivative of n) with A349134 (Dirichlet inverse of Kimberling's paraphrases).
3
0, 1, 1, 3, 1, 2, 1, 8, 4, 3, 1, 5, 1, 4, 3, 20, 1, 6, 1, 8, 4, 6, 1, 12, 7, 7, 14, 11, 1, 3, 1, 48, 6, 9, 5, 14, 1, 10, 7, 20, 1, 4, 1, 17, 8, 12, 1, 28, 10, 13, 9, 20, 1, 18, 7, 28, 10, 15, 1, 6, 1, 16, 11, 112, 8, 6, 1, 26, 12, 5, 1, 32, 1, 19, 11, 29, 8, 7, 1, 48, 46, 21, 1, 8, 10, 22, 15, 44, 1, 6, 9, 35, 16
OFFSET
1,4
COMMENTS
Dirichlet convolution of A349394 with A349432.
Dirichlet convolution with A349136 gives A300251.
LINKS
FORMULA
a(n) = Sum_{d|n} A003415(n/d) * A349134(d).
a(n) = Sum_{d|n} A349394(n/d) * A349432(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;
memoA349134 = Map();
A349134(n) = if(1==n, 1, my(v); if(mapisdefined(memoA349134, n, &v), v, v = -sumdiv(n, d, if(d<n, A003602(n/d)*A349134(d), 0)); mapput(memoA349134, n, v); (v)));
A349380(n) = sumdiv(n, d, A003415(d)*A349134(n/d));
CROSSREFS
KEYWORD
sign,look
AUTHOR
Antti Karttunen, Nov 21 2021
STATUS
approved