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

1,4

Links

Table of n, a(n) for n=1..76.

Formula

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

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 *)

Crossrefs

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

Sequence in context: A176431 A363083 A348112 * A308984 A029138 A161051

Adjacent sequences: A045744 A045745 A045746 * A045748 A045749 A045750

Keyword

nonn,easy

Author

Jeff Burch

Status

approved