A116893 Numbers k such that gcd(k!+1, k^k+1) > 1.

1, 3, 23, 39, 51, 63, 95, 99, 131, 183, 191, 215, 239, 251, 299, 303, 315, 363, 371, 411, 419, 431, 443, 495, 543, 575, 659, 683, 711, 743, 755, 791, 831, 891, 911, 935, 975, 1019, 1031, 1055, 1071, 1143, 1155, 1191, 1211, 1223, 1251, 1275, 1295, 1355

Offset: 1

Author

Giovanni Resta, Mar 01 2006

Keywords

• easy
• nonn

Comments

See A116892 for the corresponding values of the GCD. See also comments in A116891.

Examples

			gcd(1!+1, 1^1+1) = 2, gcd(2!+1, 2^2+1) = 1 and gcd(3!+1, 3^3+1) = 7, so 1 and 3 are the first two terms of the sequence.
		

Links

• Nick Hobson, Table of n, a(n) for n = 1..10000 (first 1832 terms from Antti Karttunen)
• Nick Hobson, C program.

Crossrefs

Cf. A014566, A038507, A067658, A116891, A116892, A116894.

Programs

C

See Links section.

Mathematica

Select[Range[1500], (GCD[ #!+1, #^#+1] > 1)&]

PARI

isok(n) = gcd(n! + 1, n^n + 1) != 1; \\ Michel Marcus, Jul 22 2018