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A353576
Arithmetic derivative applied to the prime shadow of the primorial base exp-function: a(n) = A003415(A181819(A276086(n))).
4
0, 1, 1, 4, 1, 5, 1, 4, 4, 12, 5, 16, 1, 5, 5, 16, 6, 21, 1, 7, 7, 24, 8, 31, 1, 9, 9, 32, 10, 41, 1, 4, 4, 12, 5, 16, 4, 12, 12, 32, 16, 44, 5, 16, 16, 44, 21, 60, 7, 24, 24, 68, 31, 92, 9, 32, 32, 92, 41, 124, 1, 5, 5, 16, 6, 21, 5, 16, 16, 44, 21, 60, 6, 21, 21, 60, 27, 81, 8, 31, 31, 92, 39, 123, 10, 41, 41, 124
OFFSET
0,4
FORMULA
a(n) = A353524(n) * A353577(n).
PROG
(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A181819(n) = factorback(apply(e->prime(e), (factor(n)[, 2])));
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
CROSSREFS
Cf. A060735 (positions of 1's).
Cf. also A353575 which has quite a similar scatter plot, while on the contrast, A353577 has a very different look, explained by the contribution of A353524.
Sequence in context: A132588 A195986 A348492 * A046785 A060044 A323413
KEYWORD
nonn,base,look
AUTHOR
Antti Karttunen, Apr 30 2022
STATUS
approved