cp's OEIS Frontend

A357428 Numbers whose digit representation in base 2 is equal to the digit representation in base 2 of the initial terms of their sets of divisors in increasing order.

%I A357428 #18 Oct 01 2022 19:18:28
%S A357428 1,6,52,63,222,2037,6776,26896,124641,220336192,222066488
%N A357428 Numbers whose digit representation in base 2 is equal to the digit representation in base 2 of the initial terms of their sets of divisors in increasing order.
%C A357428 a(1), a(2), a(3), a(8) and a(10) belong to A164894; A164894(13) = 2032242676629600594233921536, A164894(19) = 1288086824419468350412109535086131006200927555108489920512 and A164894(29) are also terms. - _Rémy Sigrist_, Sep 28 2022
%e A357428 In base 2, 6 is 110 and its first divisors are 1 and 2, that is, 1 and 10.
%o A357428 (PARI) isok(k) = my(s=[]); fordiv(k, d, s=concat(s, binary(d)); if (fromdigits(s, 2)==k, return(1)); if (fromdigits(s,2)> k, return(0)));
%o A357428 (Python)
%o A357428 from sympy import divisors
%o A357428 def ok(n):
%o A357428     target, s = bin(n)[2:], ""
%o A357428     if target[0] != "1": return False
%o A357428     for d in divisors(n):
%o A357428         s += bin(d)[2:]
%o A357428         if len(s) >= len(target): return s == target
%o A357428         elif not target.startswith(s): return False
%o A357428 print([k for k in range(10**5) if ok(k)]) # _Michael S. Branicky_, Oct 01 2022
%Y A357428 Cf. A164894, A175252 (base 10), A357429 (base 3).
%K A357428 nonn,base,more
%O A357428 1,2
%A A357428 _Michel Marcus_, Sep 28 2022
%E A357428 a(10)-a(11) from _Rémy Sigrist_, Sep 28 2022