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A374976
Odd k with p^k mod k != p for all primes p.
1
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
1,2
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).
LINKS
EXAMPLE
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.
MATHEMATICA
Cases[Range[1, 930, 2], k_/; (For[p=2, p<k && PowerMod[p, k, k]!=p, p=NextPrime[p]]; p>=k)]
KEYWORD
nonn
AUTHOR
Francois R. Grieu, Jul 26 2024
STATUS
approved