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A353577
Arithmetic derivative without its inherited divisor applied to the prime shadow of the primorial base exp-function: a(n) = A342001(A181819(A276086(n))).
4
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
FORMULA
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); };
CROSSREFS
Cf. A060735 (positions of 1's).
Cf. also A342002, A351954 (similar or analogous definitions).
Sequence in context: A236313 A222481 A351954 * A200778 A345355 A132601
KEYWORD
nonn,base,easy,look
AUTHOR
Antti Karttunen, Apr 30 2022
STATUS
approved