A114973
Numbers n such that 5^n + n^5 is a semiprime.
Original entry on oeis.org
1, 2, 4, 6, 8, 9, 84, 288, 628
Offset: 1
2 is OK because 5^2 + 2^5 = 25 + 32 = 57 = 3*19 (semiprime).
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IsSemiprime:=func< n|&+[k[2]: k in Factorization(n)] eq 2 >; [n: n in [1..85]|IsSemiprime(5^n+n^5)]; // Vincenzo Librandi, Dec 16 2010
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Select[Range[100],PrimeOmega[5^# + #^5]==2&] (* Vincenzo Librandi, May 21 2014 *)
A114974
Numbers n such that 7^n + n^7 is a semiprime.
Original entry on oeis.org
2, 12, 16, 18, 30, 39, 160, 214, 235, 408
Offset: 1
2 is in the sequence because 7^2 + 2^7 = 177 = 3*59 (semiprime).
12 is in the sequence because 7^12 + 12^7 = 13*1067470693 (semiprime). [_Vincenzo Librandi_, Dec 16 2010]
A114970
Numbers m such that 2^m + m^2 is a semiprime.
Original entry on oeis.org
5, 7, 17, 25, 43, 61, 69, 73, 105, 111, 117, 123, 135, 141, 171, 219, 231, 241, 309, 321, 543, 739, 795, 833, 975
Offset: 1
2^5 + 5^2 = 32 + 25 = 57 = 3*19 (semiprime).
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IsSemiprime:=func< n | &+[ k[2]: k in Factorization(n) ] eq 2 >; [ n: n in [1..175]|IsSemiprime(2^n+n^2)]; // Vincenzo Librandi, Dec 16 2010
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Select[Range[200], PrimeOmega[2^# + #^2]==2&] (* Vincenzo Librandi, May 21 2014 *)
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