A329617 Product of distinct exponents of prime factors of A108951(n), where A108951 is fully multiplicative with a(prime(i)) = prime(i)# = Product_{i=1..i} A000040(i).

1, 1, 1, 2, 1, 2, 1, 3, 2, 2, 1, 3, 1, 2, 2, 4, 1, 6, 1, 3, 2, 2, 1, 4, 2, 2, 3, 3, 1, 6, 1, 5, 2, 2, 2, 8, 1, 2, 2, 4, 1, 6, 1, 3, 3, 2, 1, 5, 2, 6, 2, 3, 1, 12, 2, 4, 2, 2, 1, 8, 1, 2, 3, 6, 2, 6, 1, 3, 2, 6, 1, 10, 1, 2, 6, 3, 2, 6, 1, 5, 4, 2, 1, 8, 2, 2, 2, 4, 1, 12, 2, 3, 2, 2, 2, 6, 1, 6, 3, 8, 1, 6, 1, 4, 6

Offset: 1

Author

Antti Karttunen, Nov 17 2019

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 primorial numbers

Crossrefs

Cf. A034386, A108951, A290107, A329600, A329605.

Differs from related A329378 for the first time at n=36. See also A329382.

Programs

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
A290107(n) = factorback(vecsort((factor(n)[, 2]), , 8));
A329617(n) = A290107(A108951(n));

Formula

a(n) = A290107(A108951(n)) = A290107(A329600(n)).

A329378(n) <= a(n) <= A329382(n) <= A329605(n).