A128356 Least number k > 1 (that is not the power of prime p) such that k divides (p+1)^k-1, where p = prime(n).

20, 21, 1555, 889, 253, 2041, 5846759, 148305659, 1081, 279241, 9641, 950123, 33661, 63213709997, 583223, 3775349, 72707647, 149070763, 196932497, 5091481, 25760459, 14307947980741, 13861, 9362711, 376457, 132766545553, 63757

Offset: 1

Author

Alexander Adamchuk, Mar 02 2007

Keywords

• hard
• nonn

Comments

All listed terms have 2 distinct prime divisors. Most listed terms are semiprimes, except a(7) = 20231*17^2 and a(8) = 410819*19^2. p = prime(n) divides a(n). Quotients a(n)/prime(n) are listed in A128357 = {10, 7, 311, 127, 23, 157, 343927, ...}. a(15) = 583223 = 47*12409. a(16) = 3775349 = 53*71233.

Crossrefs

Cf. A014960, A128360, A128358, A014960, A014956, A014951, A014949, A014946, A014945, A067945.

Cf. A128357 (quotients A128356(n)/prime(n)).

Programs

Mathematica

(* This program is not suitable to compute a large number of terms *) a[n_] := For[p = Prime[n]; k = 2, True, k++, If[Length[FactorInteger[k]] == 2, If[Mod[PowerMod[p + 1, k, k] - 1, k] == 0, Print[k]; Return[k]]]]; Table[a[n], {n, 1, 13}] (* Jean-François Alcover, Oct 07 2013 *)

Extensions

Terms a(14) onwards from Max Alekseyev, Feb 08 2010