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.

1, 3, 5, 17, 25, 257, 289, 65537, 66049, 4295098369

Offset: 1

Author

Jaroslav Krizek, Mar 25 2015

Keywords

• nonn
• base

Comments

Supersequence of A019434 (Fermat primes). Subsequence of A071593 and A255401.

Sequence is finite if there is only 5 Fermat primes (A019434).

Examples

			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.
		

Crossrefs

Cf. A019434, A071593, A255401.

Programs

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]));