

A253204


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


1




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



