cp's OEIS Frontend

A261436 Numbers k such that k^7-1 is a semiprime.

%I A261436 #20 Sep 08 2022 08:46:13
%S A261436 3,6,14,38,60,68,72,80,128,158,180,192,264,282,294,350,450,464,548,
%T A261436 660,710,734,798,822,878,912,942,984,998,1052,1188,1194,1224,1280,
%U A261436 1284,1382,1424,1482,1494,1512,1550,1554,1572,1608,1622,1668,1700,1710,1790,1802
%N A261436 Numbers k such that k^7-1 is a semiprime.
%C A261436 Numbers k such that k-1 and k^6+k^5+k^4+k^3+k^2+k+1 are both prime.
%C A261436 Intersection of A008864 and A100330. - _Michel Marcus_, Aug 21 2015
%H A261436 Robert Israel, <a href="/A261436/b261436.txt">Table of n, a(n) for n = 1..10000</a>
%e A261436 3 is in sequence because 3^7-1 = 2186 = 2*1093, where 2 and 1093 are both prime.
%p A261436 with(numtheory): A261436:=n->`if`(bigomega(n^7-1)=2, n, NULL): seq(A261436(n), n=1..2000); # _Wesley Ivan Hurt_, Aug 21 2015
%p A261436 select(n -> isprime(n-1) and isprime(n^6+n^5+n^4+n^3+n^2+n+1), [3,(2*i $i=2..10000)]); # _Robert Israel_, Aug 21 2015
%t A261436 Select[Range[5000], PrimeOmega[#^7 - 1] == 2 &]
%o A261436 (Magma) IsSemiprime:=func<i | &+[d[2]: d in Factorization(i)] eq 2>; [n: n in [2..5000] | IsSemiprime(s) where s is n^7- 1];
%o A261436 (PARI)  isok(n)=bigomega(n^7-1)==2 \\ _Anders Hellström_, Aug 21 2015
%Y A261436 Cf. similar sequences listed in A261435.
%Y A261436 Cf. A105041.
%Y A261436 Cf. A008864, A100330.
%K A261436 nonn,easy
%O A261436 1,1
%A A261436 _Vincenzo Librandi_, Aug 21 2015