A186525 Semiprimes of the form 7k+1.

15, 22, 57, 85, 106, 134, 141, 155, 169, 183, 218, 253, 267, 274, 295, 302, 309, 323, 358, 365, 386, 393, 407, 505, 519, 526, 533, 554, 589, 687, 694, 771, 778, 785, 799, 813, 841, 862, 869, 939, 974, 995, 1037, 1079, 1114, 1121, 1135, 1142, 1149, 1177, 1191

Offset

1,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Example

15=3*5=1+2*7, 22=2*11=1+3*7.

Mathematica

semiPrimeQ[n_] := Total[FactorInteger[n]][[2]] == 2; Select[7*Range[150] + 1, semiPrimeQ] (* Alonso del Arte, Feb 23 2011 *)
Select[7*Range[200]+1, PrimeOmega[#]==2&] (* Harvey P. Dale, Jul 27 2024 *)

Prog

(PARI) forstep(n=1, 1000, 7, bigomega(n)==2&print1(n", "))
(Magma) IsSemiprime:= func<n | &+[d[2]: d in Factorization(n)] eq 2>; [s: n in [1..200] | IsSemiprime(s) where s is 7*n + 1]; // Vincenzo Librandi, Sep 22 2012

Crossrefs

Cf. A106143 Semiprimes (mod 7).

Sequence in context: A114867 A109288 A018889 * A236107 A065728 A344134

Adjacent sequences: A186522 A186523 A186524 * A186526 A186527 A186528

Keyword

nonn

Author

Zak Seidov, Feb 23 2011

Status

approved