A329612 a(n) = gcd(d(n), d(A108951(n))), where d(n) gives the number of divisors of n, A000005(n), and A108951 is fully multiplicative with a(prime(i)) = prime(i)# = prime(1) * ... * prime(i).

1, 2, 2, 3, 2, 2, 2, 4, 3, 4, 2, 2, 2, 4, 2, 5, 2, 6, 2, 2, 4, 4, 2, 2, 3, 4, 4, 2, 2, 8, 2, 6, 4, 4, 2, 3, 2, 4, 4, 4, 2, 8, 2, 2, 2, 4, 2, 2, 3, 6, 4, 2, 2, 4, 4, 8, 4, 4, 2, 6, 2, 4, 2, 7, 4, 8, 2, 2, 4, 8, 2, 6, 2, 4, 6, 2, 2, 8, 2, 2, 5, 4, 2, 12, 4, 4, 4, 8, 2, 4, 4, 2, 4, 4, 4, 2, 2, 6, 2, 9, 2, 8, 2, 8, 8

Offset

1,2

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 primorial numbers

Formula

a(n) = gcd(A000005(n),A329605(n)) = gcd(A000005(n),A000005(A108951(n))).

Prog

(PARI)
A034386(n) = prod(i=1, primepi(n), prime(i));
A108951(n) = { my(f=factor(n)); prod(i=1, #f~, A034386(f[i, 1])^f[i, 2]) };  \\ From A108951
A329612(n) = gcd(numdiv(n), numdiv(A108951(n)));

Crossrefs

Cf. A000005, A034386, A108951, A329614.

Sequence in context: A328401 A207666 A151613 * A305980 A373152 A329601

Adjacent sequences: A329609 A329610 A329611 * A329613 A329614 A329615

Keyword

nonn

Author

Antti Karttunen, Nov 18 2019

Status

approved