This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A381922 #16 Mar 12 2025 08:09:40
%S A381922 1,2,3,4,7,8,9,63,64
%N A381922 Numbers k>0 such that the Hamming weight of k! is a factorial.
%C A381922 Also numbers k such that A000120(A000142(k)) is in A000142.
%e A381922 k = 7: A000120(A000142(7)) = 6, 6 is in A000142, thus 7 is a term.
%t A381922 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 *)
%Y A381922 Cf. A000120, A000142, A079584, A381921.
%K A381922 nonn,base,more
%O A381922 1,2
%A A381922 _Ctibor O. Zizka_, Mar 10 2025