A330690 - OEIS

%I #14 Dec 28 2019 17:01:17

%S 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,

%T 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,

%U 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

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

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

%H Antti Karttunen, <a href="/A330690/b330690.txt">Table of n, a(n) for n = 1..10201</a>

%H Antti Karttunen, <a href="/A330690/a330690.txt">Data supplement: n, a(n) computed for n = 1..65537</a>

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

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

%o (PARI)

%o A034386(n) = prod(i=1, primepi(n), prime(i));

%o A108951(n) = { my(f=factor(n)); prod(i=1, #f~, A034386(f[i, 1])^f[i, 2]) };  \\ From A108951

%o A018819(n) = if( n<1, n==0, if( n%2, A018819(n-1), A018819(n/2)+A018819(n-1))); \\ From A018819

%o A050377(n) = factorback(apply(e -> A018819(e), factor(n)[, 2]));

%o A330690(n) = A050377(A108951(n));

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

%K nonn

%O 1,4

%A _Antti Karttunen_, Dec 28 2019