A273786 Numbers n where a prime p < n exists such that n^(p-1) == 1 (mod p^2), i.e., such that p is a base-n Wieferich prime.
5, 7, 8, 9, 10, 13, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 35, 37, 38, 40, 41, 42, 43, 44, 45, 46, 48, 49, 50, 51, 53, 54, 55, 57, 60, 61, 62, 63, 64, 65, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 85, 89, 91, 93, 94
Offset: 1
Keywords
Examples
The prime 5 satisfies 24^(5-1) == 1 (mod 5^2) and 5 < 24, so 24 is a term of the sequence.
Links
- Felix Fröhlich, Table of n, a(n) for n = 1..10000
Programs
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Mathematica
Select[Range@ 94, Function[n, Count[Prime@ Range@ PrimePi@ n, p_ /; Mod[n^(p - 1), p^2] == 1] > 0]] (* Michael De Vlieger, May 30 2016 *)
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PARI
is(n) = forprime(p=1, n-1, if(Mod(n, p^2)^(p-1)==1, return(1))); 0
Comments