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A341524
Number of prime factors in A017666(n), counted with multiplicity: a(n) = bigomega(n) - bigomega(gcd(n, sigma(n))).
6
0, 1, 1, 2, 1, 0, 1, 3, 2, 1, 1, 1, 1, 1, 1, 4, 1, 2, 1, 2, 2, 1, 1, 1, 2, 1, 3, 0, 1, 1, 1, 5, 1, 1, 2, 4, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1, 1, 3, 2, 3, 1, 2, 1, 2, 2, 1, 2, 1, 1, 1, 1, 1, 3, 6, 2, 1, 1, 2, 1, 2, 1, 4, 1, 1, 3, 1, 2, 1, 1, 4, 4, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 3, 1, 3, 2, 4, 1, 1, 1, 3, 2, 1, 1, 3, 1, 2, 2, 2, 1, 1, 2, 2, 2, 1, 2, 0
OFFSET
1,4
FORMULA
a(n) = A001222(A017666(n)).
a(n) = A001222(n) - A341523(n).
MATHEMATICA
Table[PrimeOmega[n] - PrimeOmega[GCD[n, DivisorSigma[1, n]]], {n, 1, 100}] (* Amiram Eldar, Feb 17 2021 *)
PROG
(PARI) A341524(n) = (bigomega(n) - bigomega(gcd(n, sigma(n))));
CROSSREFS
Cf. A007691 (positions of zeros).
Cf. A341608 (applied onto prime shift array A246278).
Sequence in context: A343138 A119270 A267109 * A175804 A241063 A340251
KEYWORD
nonn
AUTHOR
Antti Karttunen, Feb 17 2021
STATUS
approved