A069463 -id:A069463 - cp's OEIS frontend

A069460 Greatest prime factor of prime(n)^n - 1.

2, 31, 5, 3221, 157, 25646167, 3833, 7792003, 732541, 150332843, 144061, 17615988547, 6177695707, 461017351, 31129845205681, 361353204962363828785531, 903870199, 751410597400064602523400427092397, 25058741, 153436090543, 1750258119644519

Offset: 2

Reinhard Zumkeller, Mar 24 2002

nonn

			A000040(9)^9 - 1 = 23^9 - 1 = 1801152661462 = 2*7*11*19*79*7792003, therefore a(9) = 7792003.

Hugo Pfoertner and Amiram Eldar, Table of n, a(n) for n = 2..96 (terms 2..50 from Hugo Pfoertner)
Dario Alpern, Factorization using the Elliptic Curve Method.
FactorDB, Status of 509^97-1.

Cf. A006530, A069459, A069463.

Table[FactorInteger[Prime[n]^n-1][[-1,1]],{n,2,30}] (* Harvey P. Dale, May 19 2019 *)

a(n) = A006530(A069459(n)).

More terms from Hugo Pfoertner, May 18 2004

Undefined a(1) removed by Hugo Pfoertner, Jul 22 2019

A191546 Smallest prime factor of prime(n)^n + 1 having the form 2kn+1.

Original entry on oeis.org

3, 5, 7, 1201, 13421, 28393, 22796593, 15073, 163, 421, 757241, 3512477579761, 79, 29, 24317675453761, 136593761, 21199857783625129028395239857, 37, 2494605276120959, 41, 43, 89, 691, 97, 488700001, 53, 17713, 4201, 59, 181, 2729, 449, 67, 137, 71

Offset: 1

Michel Lagneau, Jun 05 2011

nonn

			a(4) = 1201 because prime(4)^4 + 1 = 7^4+1 = 2402 = 2*1201; the prime divisor of the form 2kn + 1 is 1201 = 2*150*4 + 1 with k = 150.

Amiram Eldar, Table of n, a(n) for n = 1..82

Cf. A069463 (Greatest prime factor of prime(n)^n+1).

A191546 := proc(n) local ifs,twkn ; ifs := sort(convert(numtheory[factorset]( 1+ithprime(n)^n),list)) ; for twkn in ifs do if (twkn-1) mod (2*n) = 0 then return twkn; end if; end do: return -1 ; end proc: # R. J. Mathar, Jun 18 2011

Table[p = First /@ FactorInteger[Prime[n]^n + 1]; Select[p, Mod[#1, n] ==
  1 &, 1][[1]], {n, 1, 35}]

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A069460 Greatest prime factor of prime(n)^n - 1.

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A191546 Smallest prime factor of prime(n)^n + 1 having the form 2kn+1.

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cp's OEIS Frontend

A069460 Greatest prime factor of prime(n)^n - 1.

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Author

Keywords

Examples

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Programs

Mathematica

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Extensions

A191546 Smallest prime factor of prime(n)^n + 1 having the form 2*k*n+1.

Views

Author

Keywords

Examples

Links

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Programs

Maple

Mathematica

A191546 Smallest prime factor of prime(n)^n + 1 having the form 2kn+1.