A137664 -id:A137664 - cp's OEIS frontend

A137666 Largest prime factor of A137664(n) = (p + 1)^p - 1 for p = prime(n).

2, 7, 311, 337, 266981089, 29914249171, 7563707819165039903, 192696104561, 58769065453824529, 847499019384726257346113954958447091, 18158209813151, 138233050898929517126243814850350442620694127

Offset: 1

Alexander Adamchuk, Feb 04 2008

a(n) is also the largest prime factor of A137665(n) = A137664(n)/prime(n)^2. p^2 divides A137664(n) = (p + 1)^p - 1, p = prime(n). Least prime factors of A137664(n) are listed in A128456.

a(n) = A128456(n) = A137665(n) = ((p + 1)^p - 1)/p^2 for n = {1,2,3,7,595,...} corresponding to p = prime(n) = {2,3,5,17,4357,...} = A127837.

Amiram Eldar, Table of n, a(n) for n = 1..31 (terms 1..26 from Jens Kruse Andersen)

Cf. A128452, A128456, A128356, A128357, A137664, A137665, A128466, A127837.

FactorInteger[#][[-1,1]]&/@((#+1)^#-1&/@Prime[Range[12]]) (* Harvey P. Dale, Apr 07 2018 *)

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

Original entry on oeis.org

2, 7, 311, 42799, 6140565047, 4696537119847, 7563707819165039903, 14523213296398891966759, 105051652240885643072548950287, 8160568057655529131985731272294887039239, 47525417447024678661670292427038339608998847, 20681861558186805237407813095538883147812221153173966103

Offset: 1

Alexander Adamchuk, Feb 04 2008

nonn

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.

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

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

a(n) = my(p=prime(n)); polcyclo(p,p+1)/p \\ Hugo Pfoertner, Jul 21 2024

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

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

cp's OEIS Frontend

A137666 Largest prime factor of A137664(n) = (p + 1)^p - 1 for p = prime(n).

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