A045747 Number of prime factors of n!!!! (A007662), with multiplicity.

0, 1, 1, 2, 1, 3, 2, 5, 3, 5, 3, 8, 4, 7, 5, 12, 5, 10, 6, 15, 7, 12, 7, 19, 9, 14, 10, 22, 10, 17, 11, 27, 12, 19, 13, 31, 13, 21, 15, 35, 14, 24, 16, 38, 17, 26, 17, 43, 19, 29, 19, 46, 20, 33, 21, 50, 22, 35, 22, 54, 23, 37, 25, 60, 25, 40, 26, 63, 27, 43, 27, 68, 28, 45, 30, 71

Offset: 1

Author

Jeff Burch

Keywords

• nonn
• easy

Crossrefs

Cf. A001222 (Omega), A007662 (n!!!!).

Programs

Mathematica

NFactorialM[n_Integer, m_Integer] := Block[{k = n, p = Max[1, n]}, While[k > m, k -= m; p *= k]; p]; Table[PrimeOmega[NFactorialM[n, 4]], {n, 100}] (* Wesley Ivan Hurt, May 26 2024 after Robert G. Wilson v *)

Formula

a(n) = A001222(A007662(n)). - Wesley Ivan Hurt, May 26 2024