A261435 Numbers k such that k^5-1 is a semiprime.

12, 24, 30, 44, 62, 68, 74, 110, 164, 198, 308, 492, 572, 594, 662, 728, 770, 824, 854, 860, 864, 942, 954, 968, 1152, 1154, 1284, 1382, 1452, 1668, 1694, 1748, 1760, 1788, 1914, 2090, 2252, 2274, 2340, 2382, 2438, 2448, 2648, 2658, 2664, 2690, 2714, 2790

Offset

1,1

Comments

Numbers k such that k-1 and k^4+k^3+k^2+k+1 are both prime.

Links

Table of n, a(n) for n=1..48.

Example

a(1) = 12 because 12^5-1 = 248831 = 11*22621.

Mathematica

Select[Range[5000], PrimeOmega[#^5 - 1] == 2 &]

Prog

(Magma) IsSemiprime:=func<i | &+[d[2]: d in Factorization(i)] eq 2>; [n: n in [2..5000] | IsSemiprime(s) where s is n^5- 1];
(PARI) isok(n)=bigomega(n^5-1)==2 \\ Anders Hellström, Aug 20 2015

Crossrefs

Cf. numbers k such that k^p-1 is a semiprime, where p is prime: A096175(p=3), this sequence (p=5), A261436 (p=7), A261460 (p=11).

Cf. A104238.

Sequence in context: A082801 A328587 A328632 * A103590 A081699 A120570

Adjacent sequences: A261432 A261433 A261434 * A261436 A261437 A261438

Keyword

nonn,easy

Author

Vincenzo Librandi, Aug 20 2015

Status

approved