A329616 Bitwise-OR of exponents of prime factors of A108951(n), where A108951 is fully multiplicative with a(prime(i)) = prime(i)# = Product_{i=1..i} A000040(i).

0, 1, 1, 2, 1, 3, 1, 3, 2, 3, 1, 3, 1, 3, 3, 4, 1, 3, 1, 3, 3, 3, 1, 5, 2, 3, 3, 3, 1, 3, 1, 5, 3, 3, 3, 6, 1, 3, 3, 5, 1, 3, 1, 3, 3, 3, 1, 5, 2, 3, 3, 3, 1, 7, 3, 5, 3, 3, 1, 7, 1, 3, 3, 6, 3, 3, 1, 3, 3, 3, 1, 7, 1, 3, 3, 3, 3, 3, 1, 5, 4, 3, 1, 7, 3, 3, 3, 5, 1, 7, 3, 3, 3, 3, 3, 7, 1, 3, 3, 6, 1, 3, 1, 5, 3

Offset: 1

Author

Antti Karttunen, Nov 17 2019

Keywords

• nonn

Comments

Positions of records are: 1, 2, 4, 6, 16, 24, 36, 54, 256, 384, 576, 864, 1296, 1944, 2916, 4374, 65536, ..., conjectured also to be the positions of the first occurrence of each n.

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. A007814, A034386, A108951, A267116, A329600, A329615, A329647.

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
A267116(n) = if(n>1, fold(bitor, factor(n)[, 2]), 0); \\ From A267116
A329616(n) = A267116(A108951(n));

Formula

a(n) = A267116(A108951(n)) = A267116(A329600(n)).

a(n) >= A007814(n).

a(n) >= A329615(n).

a(n) >= A329647(n).