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

1,2

Comments

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

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

Links

Table of n, a(n) for n=1..10.

Example

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.

Prog

(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]))

Crossrefs

Cf. A019434, A071593, A255401.

Sequence in context: A323194 A024867 A025111 * A266165 A281622 A256439

Adjacent sequences: A253201 A253202 A253203 * A253205 A253206 A253207

Keyword

nonn,base

Author

Jaroslav Krizek, Mar 25 2015

Status

approved