A341519 Number of prime factors (with multiplicity) shared by A003961(n) and A003973(n): a(n) = bigomega(gcd(A003961(n), sigma(A003961(n)))).

0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 2, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 2, 0, 2, 0

Offset: 1

Author

Antti Karttunen, Feb 17 2021

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A001222, A003961, A003973, A336850, A341523.

Programs

Mathematica

f[p_, e_] := NextPrime[p]^e; g[1] = 1; g[n_] := Times @@ f @@@ FactorInteger[n]; a[n_] := PrimeOmega[GCD[(gn = g[n]), DivisorSigma[1, gn]]]; Array[a, 100] (* Amiram Eldar, Feb 17 2021 *)

PARI

A003961(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); }; \\ From A003961
A341519(n) = bigomega(gcd(A003961(n), sigma(A003961(n))));

Formula

a(n) = A001222(A336850(n)) = A001222(gcd(A003961(n), A003973(n))).

a(n) = A341523(A003961(n)).