A376567 a(n) = binomial(bigomega(n) + omega(n), omega(n)), where bigomega = A001222 and omega = A001221.

1, 2, 2, 3, 2, 6, 2, 4, 3, 6, 2, 10, 2, 6, 6, 5, 2, 10, 2, 10, 6, 6, 2, 15, 3, 6, 4, 10, 2, 20, 2, 6, 6, 6, 6, 15, 2, 6, 6, 15, 2, 20, 2, 10, 10, 6, 2, 21, 3, 10, 6, 10, 2, 15, 6, 15, 6, 6, 2, 35, 2, 6, 10, 7, 6, 20, 2, 10, 6, 20, 2, 21, 2, 6, 10, 10, 6, 20, 2

Offset: 1

Author

Michael De Vlieger, Oct 09 2024

Keywords

• nonn
• easy

Comments

For prime power p^k, a(p^k) = A010846(p^k) = A000005(p^k) = k+1. Therefore, for prime p, a(p) = A010846(p) = A000005(p) = 2.

For n in A024619, a(n) != A010846(n) and A010846(n) > A000005(n).

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A001221, A001222, A007947, A010846, A024619, A068795, A376248, A376846, A376847.

Programs

Maple

with(NumberTheory):
a := n -> binomial(Omega(n) + Omega(n, distinct), Omega(n, distinct)):
seq(a(n), n = 1..79);  # Peter Luschny, Oct 25 2024

Mathematica

Array[Binomial[#2 + #1, #1] & @@ {PrimeNu[#], PrimeOmega[#]} &, 120]

Formula

a(n) = length of row n of A376248.

a(n) = A010846(n) - A376846(n) + A376847(n).