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A352334
Composite numbers that when written in base 2 are a concatenation of their distinct prime factors without multiplicity in some order.
0
126, 7902, 58167, 63198, 119565, 505566, 507771, 2043825, 8249085, 12568150, 132992559, 183431550, 196196825, 258858950, 533713761
OFFSET
1,1
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
Sequence in context: A240929 A285172 A208618 * A267835 A202652 A278624
KEYWORD
nonn,base,more
AUTHOR
Gleb Ivanov, Mar 21 2022
EXTENSIONS
a(10)-a(15) from Amiram Eldar, Mar 21 2022
STATUS
approved