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A353379
Primepi-based variant of the arithmetic derivative applied to the prime shadow of n.
4
0, 1, 1, 2, 1, 4, 1, 3, 2, 4, 1, 7, 1, 4, 4, 4, 1, 7, 1, 7, 4, 4, 1, 11, 2, 4, 3, 7, 1, 12, 1, 5, 4, 4, 4, 12, 1, 4, 4, 11, 1, 12, 1, 7, 7, 4, 1, 15, 2, 7, 4, 7, 1, 11, 4, 11, 4, 4, 1, 20, 1, 4, 7, 6, 4, 12, 1, 7, 4, 12, 1, 19, 1, 4, 7, 7, 4, 12, 1, 15, 4, 4, 1, 20, 4, 4, 4, 11, 1, 20, 4, 7, 4, 4, 4, 21, 1, 7, 7
OFFSET
1,4
FORMULA
a(n) = A258851(A181819(n)).
MAPLE
a:= n-> (m-> m*add(i[2]*numtheory[pi](i[1])/i[1], i=ifactors(m)[2]))
(mul(ithprime(i[2]), i=ifactors(n)[2])):
seq(a(n), n=1..120); # Alois P. Heinz, Apr 28 2022
PROG
(PARI)
A181819(n) = factorback(apply(e->prime(e), (factor(n)[, 2])));
A258851(n) = (n*sum(i=1, #n=factor(n)~, n[2, i]*primepi(n[1, i])/n[1, i])); \\ From A258851
CROSSREFS
Cf. also A351942.
Sequence in context: A113901 A062799 A063647 * A263653 A330328 A269427
KEYWORD
nonn
AUTHOR
Antti Karttunen, Apr 28 2022
STATUS
approved