A376432 a(n) is the least odd prime factor of prime(n)^prime(n)+1.

5, 7, 3, 113, 3, 7, 3, 5, 3, 3, 373, 19, 3, 11, 3, 3, 3, 31, 17, 3, 37, 5, 3, 3, 7, 3, 13, 3, 5, 3, 921259, 3, 3, 5, 3, 19, 79, 41, 3, 3, 3, 7, 3, 97, 3, 5, 53, 7, 3, 5, 3, 3, 11, 3, 3, 3, 3, 17, 139, 3, 71, 3, 7, 3, 157, 3, 83, 13, 3, 5, 3, 3, 23, 11, 5, 3, 3, 199

Offset: 1

Author

Hugo Pfoertner, Sep 27 2024

Keywords

• nonn

Examples

			While almost all terms lie in the range between 3 and (prime(n)+1)/2, there are some notable outliers: a(31) = 921259 with prime(31)=127 (127^127+1=2^7*a(31)*C268), and a(1028)=1528928750837 with prime(1028)=8191 (8191^8191+1=2^13*a(1028)*C32039), Cx being composite with x decimal digits.
		

Links

• Hugo Pfoertner, Table of n, a(n) for n = 1..12250

Crossrefs

Cf. A078701, A125137, A376431.

Programs

PARI

a376432(n) = my(pp=prime(n)^prime(n)+1); forprime (p=3, oo, if(pp%p==0, return(p)))

Formula

a(n) = A078701(A125137(n)). - Michel Marcus, Sep 27 2024