A194593 Semiprimes s such that phi(s)/2 is prime.

9, 10, 14, 22, 46, 94, 118, 166, 214, 334, 358, 454, 526, 694, 718, 766, 934, 958, 1006, 1126, 1174, 1438, 1678, 1726, 1774, 1966, 2038, 2374, 2566, 2614, 2638, 2734, 2878, 2974, 3046, 3238, 3646, 3814, 4054, 4078, 4126, 4198, 4414, 4894, 4918, 5158, 5638, 5758, 5806, 5926, 5998

Offset: 1

Author

Juri-Stepan Gerasimov, Aug 30 2011

Keywords

• nonn

Comments

For n > 2, A001221(a(n)) = A001221(A000010(a(n))) = 2, and A008683(a(n)) = A008683(A000010(a(n))) = 1. - Torlach Rush, Aug 23 2018

For n > 1, A000010(a(n)) = A077065(n-1). - Torlach Rush, Sep 11 2018

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000010, A001358, A005384, A005385, A079148, A065966.

Programs

Magma

[9] cat [2*p: p in PrimesUpTo(3000) | IsPrime((p - 1) div 2)]; // Vincenzo Librandi, Aug 25 2018

Maple

9, 10, op(select(s -> isprime(s/2) and isprime((s-2)/4), [seq(s,s=6..10000,8)])); # Robert Israel, Apr 06 2016

Mathematica

Select[Range@ 6000, PrimeOmega@ # == 2 && PrimeQ[EulerPhi[#]/2] &] (* Michael De Vlieger, Apr 06 2016 *)

PARI

isok(n) = (bigomega(n)== 2) && isprime(eulerphi(n)/2); \\ Michel Marcus, Apr 06 2016

Formula

a(n) = 2*A005385(n-1), n>1.

a(n) = 4*A005384(n-1) + 2, n > 1. - Michel Marcus, Apr 02 2020

Extensions

Corrected by R. J. Mathar, Oct 13 2011