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%I #32 Apr 25 2022 01:44:17
%S 126,7902,58167,63198,119565,505566,507771,2043825,8249085,12568150,
%T 132992559,183431550,196196825,258858950,533713761
%N Composite numbers that when written in base 2 are a concatenation of their distinct prime factors without multiplicity in some order.
%e 126_10 = 1111110_2 = 2*3^2*7, and 1111110 = 11.111.10, where "." represents concatenation.
%t q[n_] := CompositeQ[n] && MemberQ[Join @@@ Permutations @ IntegerDigits[ FactorInteger[n][[;; , 1]], 2], IntegerDigits[n, 2]]; Select[Range[600000], q] (* _Amiram Eldar_, Mar 21 2022 *)
%o (Python)
%o from sympy import primefactors
%o from itertools import permutations
%o for i in range(1, 10**12):
%o p = primefactors(i)
%o if len(p) != 1:
%o p = list(map(lambda x: format(x, 'b'),p))
%o if all(j in format(i,'b') for j in p) and any(format(i,'b')==''.join(t) for t in permutations(p)):
%o print(i, end = ', ')
%Y Cf. A324260, A324257.
%K nonn,base,more
%O 1,1
%A _Gleb Ivanov_, Mar 21 2022
%E a(10)-a(15) from _Amiram Eldar_, Mar 21 2022
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