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A345000
a(n) = gcd(A003415(n), A003415(A276086(n))), where A003415(n) is the arithmetic derivative of n, and A276086(n) gives the prime product form of primorial base expansion of n.
20
0, 1, 1, 1, 2, 1, 1, 1, 4, 1, 1, 1, 2, 1, 1, 1, 16, 1, 3, 1, 2, 5, 1, 1, 4, 5, 5, 1, 2, 1, 1, 1, 10, 1, 1, 3, 12, 1, 1, 1, 2, 1, 1, 1, 4, 1, 5, 1, 2, 1, 5, 5, 4, 1, 3, 1, 2, 1, 1, 1, 2, 1, 1, 1, 12, 3, 1, 1, 2, 1, 1, 1, 12, 1, 1, 55, 10, 3, 1, 1, 16, 1, 1, 1, 2, 1, 5, 1, 140, 1, 3, 1, 16, 1, 49, 3, 2, 1, 7, 1, 28, 1, 7, 1, 2, 1
OFFSET
0,5
FORMULA
a(n) = gcd(A003415(n), A327860(n)) = gcd(A003415(n), A003415(A276086(n))).
PROG
(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A345000(n) = gcd(A003415(n), A003415(A276086(n)));
CROSSREFS
Cf. A003415, A276086, A327860, A347958 (inverse Möbius transform), A347959, A351083, A351085, A351086, A351235, A351236.
Cf. A166486 (a(n) mod 2, parity of terms, see comment in A327860).
Cf. also A324198, A327858.
Sequence in context: A343370 A160467 A353573 * A352894 A122374 A261960
KEYWORD
nonn,base,easy,look
AUTHOR
Antti Karttunen, Jul 21 2021
STATUS
approved