A128357 Quotients A128356(n)/prime(n).

10, 7, 311, 127, 23, 157, 343927, 7805561, 47, 9629, 311, 25679, 821, 1470086279, 12409, 71233, 1232333, 2443783, 2939291, 71711, 352883, 181113265579, 167, 105199, 3881, 1314520253, 619, 20759, 117503, 1162660843, 1880415721, 263

Offset: 1

Author

Alexander Adamchuk, Mar 02 2007, Mar 09 2007

Keywords

• hard
• nonn

Comments

A128356 = {20, 21, 1555, 889, 253, 2041, 5846759, ...} = Least number k>1 (that is not the power of prime p) such that k divides (p+1)^k-1, where p = prime(n). Most listed terms are primes, except a(7) = 20231*17 and a(8) = 410819*19. a(15) = 12409. a(16) = 71233.

Note that all prime listed terms of {a(n)} coincide with terms of A128456 = {2, 7, 311, 127, 23, 157, 7563707819165039903, 75368484119, 47, 9629, 311, 25679, 821, ...} = least prime factor of ((p+1)^p - 1)/p^2, where p = prime(n).

Crossrefs

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

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

Cf. A128456 (least prime factor of ((p+1)^p - 1)/p^2, where p = prime(n)).

Extensions

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