1,1

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(n) = {2,7,311,337,266981089,29914249171,7563707819165039903,...}. a(n) is prime for n = {1,2,3,7,595,...} corresponding to p = prime(n) = {2,3,5,17,4357,...} = A127837. Primes in a(n) are {2,7,311,7563707819165039903,...} = A128466.

a(n) = ((prime[n] + 1)^prime[n] - 1)/prime[n]^2; a(n) = A137664(n)/prime[n]^2.

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

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

Sequence in context: A012987 A128456 A137666 this_sequence A128466 A048122 A144787

Adjacent sequences: A137662 A137663 A137664 this_sequence A137666 A137667 A137668

nonn

Alexander Adamchuk (alex(AT)kolmogorov.com), Feb 04 2008