login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Numbers k such that k^11-1 is a semiprime.
1

%I #13 Sep 08 2022 08:46:13

%S 2,20,30,60,212,224,258,272,390,398,480,504,654,770,812,1040,1194,

%T 1448,1698,1748,1874,2000,2238,2274,2294,2438,2522,2664,2714,2790,

%U 2802,3020,3138,3168,3300,3392,3434,3794,4160,4232,4518,4722,4968,5334,5654,5658

%N Numbers k such that k^11-1 is a semiprime.

%C After 2, numbers k such that k-1 and k^10 + k^9 + k^8 + k^7 + k^6 + k^5 + k^4 + k^3 + k^2 + k + 1 are both prime.

%C Intersection of A008864 and A162862. - _Michel Marcus_, Aug 21 2015

%e 20 is in sequence because 20^11-1 = 204799999999999 = 19*10778947368421, where 19 and 10778947368421 are both prime.

%t Select[Range[6000], PrimeOmega[#^11 - 1] == 2 &]

%o (Magma) IsSemiprime:=func<i | &+[d[2]: d in Factorization(i)] eq 2>; [n: n in [2..4000] | IsSemiprime(s) where s is n^11- 1];

%o (PARI) isok(n)=bigomega(n^11-1)==2 \\ _Anders Hellström_, Aug 21 2015

%Y Cf. similar sequences listed in A261435.

%Y Cf. A105122.

%Y Cf. A008864, A162862.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Aug 21 2015