A137665 Quotients ((p+1)^p - 1)/p^2 for p = prime(n).

2, 7, 311, 42799, 6140565047, 4696537119847, 7563707819165039903, 14523213296398891966759, 105051652240885643072548950287, 8160568057655529131985731272294887039239

Offset

1,1

Comments

p^2 divides a(n) = (p+1)^p - 1, p = prime(n). (p+1)^p - 1 = A137664(n) = {8, 63, 7775, 2097151, 743008370687, 793714773254143, 2185911559738696531967, ...}.

Least prime factors of a(n) are listed in A128456(n) = {2, 7, 311, 127, 23, 157, 7563707819165039903, ...}.

Largest prime factors a(n) are listed in A137666.

a(n) is prime for n = {1, 2, 3, 7, 595, ...} corresponding to p = prime(n) = {2, 3, 5, 17, 4357, ...} = A127837.

Primes in this sequence are A128466.

Links

Table of n, a(n) for n=1..10.

Formula

a(n) = ((prime(n) + 1)^prime(n) - 1)/prime(n)^2;

a(n) = A137664(n)/prime(n)^2.

Mathematica

Table[ ((Prime[n] + 1)^Prime[n] - 1)/Prime[n]^2, {n, 1, 15} ]

Crossrefs

Cf. A128452, A128456, A128356, A128466, A127837, A128357, A060073, A137664, A137666.

Sequence in context: A367788 A128456 A137666 * A128466 A048122 A144787

Adjacent sequences: A137662 A137663 A137664 * A137666 A137667 A137668

Keyword

nonn

Author

Alexander Adamchuk, Feb 04 2008

Status

approved