A381922 Numbers k>0 such that the Hamming weight of k! is a factorial.

1, 2, 3, 4, 7, 8, 9, 63, 64

Offset: 1

Author

Ctibor O. Zizka, Mar 10 2025

Keywords

• nonn
• base
• more

Comments

Also numbers k such that A000120(A000142(k)) is in A000142.

Examples

			k = 7: A000120(A000142(7)) = 6, 6 is in A000142, thus 7 is a term.
		

Crossrefs

Cf. A000120, A000142, A079584, A381921.

Programs

Mathematica

factorialQ[n_] := factorialQ[n] = Module[{m = n, k = 2}, While[Divisible[m, k], m /= k; k++]; m == 1]; q[n_] := factorialQ[DigitCount[n!, 2, 1]]; Select[Range[100], q] (* Amiram Eldar, Mar 10 2025 *)