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A341523
Number of prime factors (with multiplicity) shared by n and sigma(n): a(n) = bigomega(gcd(n, sigma(n))).
4
0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 2, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 3, 0, 1, 0, 3, 0, 2, 0, 0, 1, 1, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 1, 1, 0, 2, 0, 0, 1, 1, 0, 2, 0, 3, 0, 1, 0, 3, 0, 1, 0, 0, 0, 2, 0, 1, 1, 1, 0, 1, 0, 1, 0, 2, 0, 2, 0, 1, 0, 1, 0, 3, 0, 1, 1, 2, 0, 3, 1, 2, 0, 1, 1, 3, 0, 0, 1, 0, 0, 2, 0, 1, 1
OFFSET
1,6
FORMULA
a(n) = A001222(A009194(n)).
a(n) = A001222(n) - A341524(n).
a(A003961(n)) = A341519(n).
MATHEMATICA
Table[PrimeOmega[GCD[n, DivisorSigma[1, n]]], {n, 1, 100}] (* Amiram Eldar, Feb 17 2021 *)
PROG
(PARI) A341523(n) = bigomega(gcd(n, sigma(n)));
CROSSREFS
Cf. A000203, A003961, A009194, A014567 (positions of zeros), A341519, A341524.
Sequence in context: A070138 A024153 A354527 * A079127 A056674 A349798
KEYWORD
nonn
AUTHOR
Antti Karttunen, Feb 17 2021
STATUS
approved