A353577 Arithmetic derivative without its inherited divisor applied to the prime shadow of the primorial base exp-function: a(n) = A342001(A181819(A276086(n))).

0, 1, 1, 2, 1, 5, 1, 2, 2, 3, 5, 8, 1, 5, 5, 8, 2, 7, 1, 7, 7, 12, 8, 31, 1, 9, 9, 16, 10, 41, 1, 2, 2, 3, 5, 8, 2, 3, 3, 4, 8, 11, 5, 8, 8, 11, 7, 10, 7, 12, 12, 17, 31, 46, 9, 16, 16, 23, 41, 62, 1, 5, 5, 8, 2, 7, 5, 8, 8, 11, 7, 10, 2, 7, 7, 10, 3, 9, 8, 31, 31, 46, 13, 41, 10, 41, 41, 62, 17, 55, 1, 7, 7, 12, 8

Offset

0,4

Links

Antti Karttunen, Table of n, a(n) for n = 0..11550

Index entries for sequences related to primorial base

Formula

a(n) = A342001(A328835(n)) = A351945(A276086(n)) = A342001(A181819(A276086(n))).

a(n) = A353576(n) / A353524(n).

Prog

(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A003557(n) = (n/factorback(factorint(n)[, 1]));
A342001(n) = (A003415(n) / A003557(n));
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); };
A353577(n) = A342001(A181819(A276086(n)));

Crossrefs

Cf. A003415, A003557, A181819, A276086, A328835, A342001, A351942, A351945, A353524, A353576.

Cf. A060735 (positions of 1's).

Cf. also A342002, A351954 (similar or analogous definitions).

Sequence in context: A236313 A222481 A351954 * A200778 A345355 A132601

Adjacent sequences: A353574 A353575 A353576 * A353578 A353579 A353580

Keyword

nonn,base,easy,look

Author

Antti Karttunen, Apr 30 2022

Status

approved