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A317138 Numbers k such that (2k)^3 - 1 is a semiprime. 1
3, 4, 6, 7, 10, 12, 19, 27, 31, 40, 45, 55, 69, 75, 82, 84, 96, 97, 136, 139, 157, 166, 174, 199, 201, 217, 250, 286, 321, 322, 360, 364, 381, 399, 406, 430, 432, 439, 460, 496, 510, 511, 535, 546, 549, 559, 565, 591, 601, 615, 630, 654, 717, 720, 724, 727, 742 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Numbers k such that 2k - 1 and 4k^2 + 2k + 1 are both prime.

LINKS

K. D. Bajpai, Table of n, a(n) for n = 1..9443

FORMULA

a(n) = A096175(n)/2 = 1/2*(A242262(n) + 1)^(1/3).

EXAMPLE

From K. D. Bajpai, Nov 16 2019: (Start)

a(3) = 6 is a term because (2*6)^3-1 = 1727 = 11*157 that is a semiprime.

a(4) = 7 is a term because (2*7)^3-1 = 2743 = 13*211 that is a semiprime.

9 is not in the sequence because (2*9)^3-1 = 5831 = 7*7*7*17 that is not semiprime.

(End)

MAPLE

issp:= n-> not isprime(n) and numtheory[bigomega](n)=2:

select( n-> issp((2*n)^3-1),  [seq(n, n=1..200)]); # K. D. Bajpai, Nov 16 2019

MATHEMATICA

Select[Range@ 750, PrimeOmega[(2 #)^3 - 1] == 2 &] (* Michael De Vlieger, Aug 02 2018 *)

PROG

(PARI) for(k=1, 500, if(bigomega((2*k)^3-1)==2, print1(k, ", ")))

(MAGMA) IsSemiprime:=func<i | &+[d[2]: d in Factorization(i)] eq 2>; [n: n in [2..800] | IsSemiprime(s) where s is (2*n)^3-1]; // Vincenzo Librandi, Aug 04 2018

CROSSREFS

Cf. A096175, A242262.

Cf. A237037 (numbers k such that (2k)^3 + 1 is a semiprime).

Sequence in context: A147609 A202169 A239438 * A032387 A026313 A024912

Adjacent sequences:  A317135 A317136 A317137 * A317139 A317140 A317141

KEYWORD

nonn

AUTHOR

Jianing Song, Aug 01 2018

STATUS

approved

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Last modified May 9 19:23 EDT 2021. Contains 343746 sequences. (Running on oeis4.)