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A177087 Semiprimes of the form n^5-n^3-2*n^2+1. 1

%I #12 Sep 08 2022 08:45:53

%S 2951,16367,58159,159479,368759,534689,1414367,2468519,3191201,

%T 11862449,14327767,20485079,28597439,45393809,102332801,115783919,

%U 130613617,146925239,282352799,312370001,344887399,418040999,459001729

%N Semiprimes of the form n^5-n^3-2*n^2+1.

%H Vincenzo Librandi, <a href="/A177087/b177087.txt">Table of n, a(n) for n = 1..1000</a>

%e 2951=5^5-5^3-2*5^2+1 is in the sequence because 2951=13*227 and 13, 227 are primes;

%e 58159=9^5-9^3-2*9^2+1 is in the sequence because 58159=19*3061 and 19, 3061 are primes, etc.

%t f[n_] := Last/@FactorInteger[n] == {1,1}; Select[Array[#^5 - #^3 - 2*#^2 + 1 &, 100], f[#] &] (* _Vincenzo Librandi_, Sep 21 2012 *)

%t Select[Table[n^5 - n^3 - 2 n^2 + 1, {n, 60}], PrimeOmega[#] == 2 &] (* _Bruno Berselli_, Sep 21 2012 *)

%o (Magma) IsSemiprime:=func<n | &+[d[2]: d in Factorization(n)] eq 2>; [s: n in [2..60] | IsSemiprime(s) where s is n^5-n^3-2*n^2+1]; // _Bruno Berselli_, Sep 21 2012

%Y Cf. A177075, A177076, A177088 (associated n).

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Jun 05 2010

%E Checked by Jud McCranie, Jun 16 2010

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Last modified July 18 21:02 EDT 2024. Contains 374388 sequences. (Running on oeis4.)