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

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

Offset

1,1

Comments

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, ...}.

Links

Table of n, a(n) for n=1..10.

Formula

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

Mathematica

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

Crossrefs

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

Sequence in context: A353993 A189943 A358324 * A317028 A014392 A008462

Adjacent sequences: A137661 A137662 A137663 * A137665 A137666 A137667

Keyword

nonn

Author

Alexander Adamchuk, Feb 04 2008

Status

approved