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A268574 Numbers n such that (2^n+1)^2-2 is a semiprime. 1
4, 6, 7, 10, 11, 14, 22, 36, 38, 39, 44, 45, 48, 49, 60, 72, 74, 75, 89, 92, 96, 99, 105, 110, 111, 113, 116, 131, 138, 143, 150, 170, 173, 182, 194, 201, 212, 234, 260 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(40) >= 282. - Hugo Pfoertner, Aug 05 2019

LINKS

Table of n, a(n) for n=1..39.

factordb.com, Status of (2^282+1)^2-2.

EXAMPLE

a(1) = 4 because 17^2-2 = 287 = 7*41, which is semiprime.

a(2) = 6 because 65^2-2 = 4223 = 41*103, which is semiprime.

MATHEMATICA

Select[Range[105], PrimeOmega[(2^# + 1)^2 - 2] == 2 &]

PROG

(MAGMA) IsSemiprime:=func<i | &+[d[2]: d in Factorization(i)] eq 2>; [n: n in [1..110]| IsSemiprime(s) where s is (2^n+1)^2-2];

(PARI) isok(n) = bigomega((2^n+1)^2-2) == 2; \\ Michel Marcus, Feb 22 2016

CROSSREFS

Cf. A091513, A091514, A093069, A269264.

Sequence in context: A032785 A096887 A340161 * A023631 A080641 A272632

Adjacent sequences:  A268571 A268572 A268573 * A268575 A268576 A268577

KEYWORD

nonn,more,hard

AUTHOR

Vincenzo Librandi, Feb 21 2016

EXTENSIONS

a(25)-a(39) from Hugo Pfoertner, Aug 05 2019

STATUS

approved

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Last modified August 7 23:50 EDT 2022. Contains 355995 sequences. (Running on oeis4.)