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A253204 a(1) = 1; for n>1, a(n) is a prime power p^h (h>=1) with the property that its k-th smallest divisor, for all 1 <= k <= tau(p^h), contains exactly k "1" digits in its binary representation.

%I A253204 #12 May 23 2025 18:24:10
%S A253204 1,3,5,17,25,257,289,65537,66049,4295098369
%N A253204 a(1) = 1; for n>1, a(n) is a prime power p^h (h>=1) with the property that its k-th smallest divisor, for all 1 <= k <= tau(p^h), contains exactly k "1" digits in its binary representation.
%C A253204 Supersequence of A019434 (Fermat primes). Subsequence of A071593 and A255401.
%C A253204 Sequence is finite if there is only 5 Fermat primes (A019434).
%e A253204 The divisors of 4295098369, expressed in base 2 and listed in ascending order as 1, 10000000000000001, 100000000000000100000000000000001, contain 1, 2 and 3, "1" digits, respectively.
%o A253204 (Magma) Set(Sort([1] cat [n: n in [2..1000000] | [&+Intseq(d, 2): d in Divisors(n)] eq [1..NumberOfDivisors(n)] and #(PrimeDivisors(n)) eq 1]));
%Y A253204 Cf. A019434, A071593, A255401.
%K A253204 nonn,base
%O A253204 1,2
%A A253204 _Jaroslav Krizek_, Mar 25 2015