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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 7 12:19 EDT 2020. Contains 336276 sequences. (Running on oeis4.)