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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, 47525417447024678661670292427038339608998847, 20681861558186805237407813095538883147812221153173966103
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.
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} ]
PROG
(PARI) a(n) = my(p=prime(n)); polcyclo(p, p+1)/p \\ Hugo Pfoertner, Jul 21 2024
KEYWORD
nonn
AUTHOR
Alexander Adamchuk, Feb 04 2008
STATUS
approved