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%I #15 Mar 12 2025 08:09:10
%S 1,2,6,24,5040,40320,362880,
%T 1982608315404440064116146708361898137544773690227268628106279599612729753600000000000000,
%U 126886932185884164103433389335161480802865516174545192198801894375214704230400000000000000
%N Factorial numbers whose Hamming weight is also a factorial number.
%F a(n) = A000142(A381922(n)).
%e k = 7: A000120(A000142(7)) = 6, 6 is from A000142, thus 7! is a term.
%t With[{f = Range[100]!}, Select[f, MemberQ[f, DigitCount[#, 2, 1]] &]] (* _Amiram Eldar_, Mar 10 2025 *)
%Y Cf. A000120, A000142, A381922.
%K nonn,base
%O 1,2
%A _Ctibor O. Zizka_, Mar 10 2025