A181591 a(n) = binomial(bigOmega(n),omega(n)), where omega = A001221 and bigOmega = A001222.

1, 1, 1, 2, 1, 1, 1, 3, 2, 1, 1, 3, 1, 1, 1, 4, 1, 3, 1, 3, 1, 1, 1, 6, 2, 1, 3, 3, 1, 1, 1, 5, 1, 1, 1, 6, 1, 1, 1, 6, 1, 1, 1, 3, 3, 1, 1, 10, 2, 3, 1, 3, 1, 6, 1, 6, 1, 1, 1, 4, 1, 1, 3, 6, 1, 1, 1, 3, 1, 1, 1, 10, 1, 1, 3, 3, 1, 1, 1, 10, 4, 1, 1, 4, 1, 1, 1, 6, 1, 4, 1, 3, 1, 1, 1, 15, 1, 3, 3, 6

Offset: 1

Author

Reinhard Zumkeller, Nov 01 2010

Keywords

• nonn

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Index entries for sequences computed from exponents in factorization of n

Crossrefs

Cf. A001221, A001222, A007318, A136277.

Cf. A088529, A136565 (equal for n = 2..23).

Programs

Mathematica

a[n_] := Binomial[PrimeOmega[n], PrimeNu[n]]; Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Jun 29 2013 *)

PARI

a(n) = binomial(bigomega(n), omega(n)); \\ Michel Marcus, Jul 10 2022

Formula

a(n) = A007318(A001222(n),A001221(n)).

a(n) = A088529(n) = A136565(n) for 2 <= n < 24.

a(n) = A136277(A156552(n)). - Antti Karttunen, May 29 2017