A374976 Odd k with p^k mod k != p for all primes p.

1, 9, 27, 63, 75, 81, 115, 119, 125, 189, 207, 209, 215, 235, 243, 279, 299, 319, 323, 387, 407, 413, 423, 515, 517, 531, 535, 551, 567, 575, 583, 611, 621, 623, 667, 675, 707, 713, 729, 731, 747, 767, 779, 783, 799, 815, 835, 851, 869, 893, 899, 917, 923, 927

Offset: 1

Author

Francois R. Grieu, Jul 26 2024

Keywords

• nonn

Comments

Alternatively: 1, and odd composites not a pseudoprime to any prime base.

The sequence contains no primes, no pseudoprimes to any prime base (A001567, A005935, A005936, A005938, A020139, A020141...), and no Carmichael numbers (A002997).

Examples

			k=3 (resp. 5, 7) is not in the sequence because for prime p=2 it holds p^k mod k = 2 which is p.
k=9 is in the sequence because for prime p=2 (resp. 3, 5, 7) it holds p^k mod k = 8 (resp. 0, 8, 1) which is not p, and for all other primes p it holds p>=k therefore p^k mod k can't be p.
		

Links

• Francois R. Grieu, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A001567, A005935, A005936, A005938, A020139, A020141, A020145, A002997.

Programs

Mathematica

Cases[Range[1, 930, 2], k_/; (For[p=2, p=k)]