

A269264


Numbers k such that (2^k1)^2  2 is a semiprime.


1



5, 9, 13, 16, 23, 24, 28, 35, 37, 38, 40, 47, 48, 51, 52, 57, 61, 65, 67, 70, 79, 83, 84, 85, 88, 90, 102, 111, 144, 148, 157, 162, 168, 169, 177, 181, 190, 237, 246, 298, 308, 346
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OFFSET

1,1


COMMENTS

a(43) >= 360.  Hugo Pfoertner, Aug 05 2019


LINKS

Table of n, a(n) for n=1..42.
factordb.com, Status of (2^3601)^22.


EXAMPLE

a(1) = 5 because 31^22 = 959 = 7*137 which is semiprime.
a(2) = 9 because 511^22 = 261119 = 23*11353 which is semiprime.


MATHEMATICA

Select[Range[120], PrimeOmega[(2^#  1)^2  2] == 2 &]


PROG

(MAGMA) IsSemiprime:=func<i  &+[d[2]: d in Factorization(i)] eq 2>; [n: n in [2..120] IsSemiprime(s) where s is (2^n1)^22];
(PARI) isok(n) = bigomega((2^n1)^22) == 2; \\ Michel Marcus, Feb 22 2016


CROSSREFS

Cf. A091515, A091516, A268574.
Sequence in context: A281582 A190696 A314662 * A314663 A314664 A051541
Adjacent sequences: A269261 A269262 A269263 * A269265 A269266 A269267


KEYWORD

nonn,more,hard


AUTHOR

Vincenzo Librandi, Feb 21 2016


EXTENSIONS

a(29)a(42) from Hugo Pfoertner, Aug 05 2019


STATUS

approved



