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A137665 Quotients ((p + 1)^p - 1)/p^2 for p = prime[n]. 2
2, 7, 311, 42799, 6140565047, 4696537119847, 7563707819165039903, 14523213296398891966759, 105051652240885643072548950287, 8160568057655529131985731272294887039239 (list; graph; refs; listen; history; text; internal format)
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(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.

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: A260967 A128456 A137666 * A128466 A048122 A144787

Adjacent sequences:  A137662 A137663 A137664 * A137666 A137667 A137668

KEYWORD

nonn

AUTHOR

Alexander Adamchuk, Feb 04 2008

STATUS

approved

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Last modified February 18 05:35 EST 2019. Contains 320245 sequences. (Running on oeis4.)