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

1,24

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)

Formula

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

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

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 *)

Prog

(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))));

Crossrefs

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

Sequence in context: A070092 A365545 A342770 * A307837 A123671 A191261

Adjacent sequences: A341516 A341517 A341518 * A341520 A341521 A341522

Keyword

nonn

Author

Antti Karttunen, Feb 17 2021

Status

approved