A330690 Number of ways to factor A108951(n) into "Fermi-Dirac primes" (A050376), where A108951 is fully multiplicative with a(prime(k)) = k-th primorial.

1, 1, 1, 2, 1, 2, 1, 2, 4, 2, 1, 2, 1, 2, 4, 4, 1, 4, 1, 2, 4, 2, 1, 4, 8, 2, 4, 2, 1, 4, 1, 4, 4, 2, 8, 8, 1, 2, 4, 4, 1, 4, 1, 2, 4, 2, 1, 4, 16, 8, 4, 2, 1, 8, 8, 4, 4, 2, 1, 8, 1, 2, 4, 6, 8, 4, 1, 2, 4, 8, 1, 8, 1, 2, 8, 2, 16, 4, 1, 4, 16, 2, 1, 8, 8, 2, 4, 4, 1, 8, 16, 2, 4, 2, 8, 6, 1, 16, 4, 16, 1, 4, 1, 4, 8

Offset: 1

Author

Antti Karttunen, Dec 28 2019

Keywords

• nonn

Comments

a(64) = 6 is the first term which is not a power of 2.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10201
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Crossrefs

Cf. A034386, A018819, A050376, A050377, A050378, A108951, A329901.

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
A018819(n) = if( n<1, n==0, if( n%2, A018819(n-1), A018819(n/2)+A018819(n-1))); \\ From A018819
A050377(n) = factorback(apply(e -> A018819(e), factor(n)[, 2]));
A330690(n) = A050377(A108951(n));

Formula

a(n) = A050377(A108951(n)).

a(n) = A050378(A329901(n)).