A329601 The squarefree kernel of Product prime(e(i)), when n = Product prime(i)^e(i).

1, 2, 2, 3, 2, 2, 2, 5, 3, 2, 2, 6, 2, 2, 2, 7, 2, 6, 2, 6, 2, 2, 2, 10, 3, 2, 5, 6, 2, 2, 2, 11, 2, 2, 2, 3, 2, 2, 2, 10, 2, 2, 2, 6, 6, 2, 2, 14, 3, 6, 2, 6, 2, 10, 2, 10, 2, 2, 2, 6, 2, 2, 6, 13, 2, 2, 2, 6, 2, 2, 2, 15, 2, 2, 6, 6, 2, 2, 2, 14, 7, 2, 2, 6, 2, 2, 2, 10, 2, 6, 2, 6, 2, 2, 2, 22, 2, 6

Offset: 1

Author

Antti Karttunen, Nov 19 2019

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..100000
• Index entries for sequences computed from exponents in factorization of n

Crossrefs

Cf. A007947, A019565, A108951, A181819, A181821, A297404, A328400, A329607.

Programs

PARI

A007947(n) = factorback(factorint(n)[, 1]);
A181819(n) = {my(f=factor(n)); prod(k=1, #f~, prime(f[k, 2])); }; \\ From A181819
A329601(n) = A007947(A181819(n));

Formula

a(n) = A007947(A181819(n)).

a(n) = A181819(A328400(n)), A181821(a(n)) = A328400(n).

a(A108951(n)) = A329607(n).

a(n) = A019565(A297404(n)). - Peter Munn, Oct 02 2023