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Composite numbers that when written in base 2 are a concatenation of their distinct prime factors without multiplicity in some order.
0

%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