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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.
1
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).
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
KEYWORD
nonn,base
AUTHOR
Jaroslav Krizek, Mar 25 2015
STATUS
approved