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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 30 10:14 EDT 2022. Contains 354921 sequences. (Running on oeis4.)