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

1,1

Links

Table of n, a(n) for n=1..15.

Example

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

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 *)

Prog

(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 = ', ')

Crossrefs

Cf. A324260, A324257.

Sequence in context: A240929 A285172 A208618 * A267835 A202652 A278624

Adjacent sequences: A352331 A352332 A352333 * A352335 A352336 A352337

Keyword

nonn,base,more

Author

Gleb Ivanov, Mar 21 2022

Extensions

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

Status

approved