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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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 LINKS Antti Karttunen, Table of n, a(n) for n = 1..65537 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: A070201 A070138 A024153 * A079127 A056674 A336107 Adjacent sequences:  A341520 A341521 A341522 * A341524 A341525 A341526 KEYWORD nonn AUTHOR Antti Karttunen, Feb 17 2021 STATUS approved

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Last modified April 10 11:15 EDT 2021. Contains 342845 sequences. (Running on oeis4.)