A137666 -id:A137666 - cp's OEIS frontend

A137664 a(n) = (p+1)^p - 1 where p = prime(n).

8, 63, 7775, 2097151, 743008370687, 793714773254143, 2185911559738696531967, 5242879999999999999999999, 55572324035428505185378394701823, 6863037736488299999999999999999999999999999

Offset: 1

Alexander Adamchuk, Feb 04 2008

nonn

p^2 divides a(n) = (p+1)^p - 1, p = prime(n).
Quotients a(n)/prime(n)^2 are listed in A137665(n) = {2, 7, 311, 42799, 6140565047, 4696537119847, 7563707819165039903, ...}.
Least prime factors of A137665(n) = a(n)/prime(n)^2 are listed in A128456(n) = {2, 7, 311, 127, 23, 157, 7563707819165039903, ...}.
Largest prime factors A137665(n) = a(n)/prime(n)^2 are listed in A137666(n) = {2, 7, 311, 337, 266981089, 29914249171, 7563707819165039903, ...}.

Cf. A128452, A128456, A128356, A128357, A137665, A137666.

Table[ (Prime[n] + 1)^Prime[n] - 1, {n,1,15} ]
(#+1)^#-1&/@Prime[Range[10]] (* Harvey P. Dale, Jan 10 2025 *)

a(n) = (prime(n) + 1)^prime(n) - 1.

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

A137664 a(n) = (p+1)^p - 1 where p = prime(n).

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica

Formula