A352334 Composite numbers that when written in base 2 are a concatenation of their distinct prime factors without multiplicity in some order.

126, 7902, 58167, 63198, 119565, 505566, 507771, 2043825, 8249085, 12568150, 132992559, 183431550, 196196825, 258858950, 533713761

Offset: 1

Author

Gleb Ivanov, Mar 21 2022

Keywords

• nonn
• base
• more

Examples

			126_10 = 1111110_2 = 2*3^2*7, and 1111110 = 11.111.10, where "." represents concatenation.
		

Crossrefs

Cf. A324260, A324257.

Programs

Mathematica

q[n_] := CompositeQ[n] && MemberQ[Join @@@ Permutations @ IntegerDigits[ FactorInteger[n][[;; , 1]], 2], IntegerDigits[n, 2]]; Select[Range[600000], q] (* Amiram Eldar, Mar 21 2022 *)

Python

from sympy import primefactors
from itertools import permutations
for i in range(1, 10**12):
    p = primefactors(i)
    if len(p) != 1:
        p = list(map(lambda x: format(x, 'b'),p))
        if all(j in format(i,'b') for j in p) and any(format(i,'b')==''.join(t) for t in permutations(p)):
            print(i, end = ', ')

Extensions

a(10)-a(15) from Amiram Eldar, Mar 21 2022