

A096082


Smallest odd prime p such that p^2  n^(p1)  1.


9



3, 1093, 11, 1093, 20771, 66161, 5, 3, 11, 3, 71, 2693, 863, 29, 29131, 1093, 3, 5, 3, 281
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OFFSET

1,1


COMMENTS

Similar to the sequence A039951 where p=2 is allowed.
a(n^k) <= a(n) for any n,k>1.
a(21) > 1.63*10^14 (see Fischer's link).
For all nonnegative integers n and k, a(n^(n^k)) = a(n). (see puzzle 762 in the links). Also a(n) = 3 if and only if mod(n, 36) is in the set {1, 8, 10, 19, 26, 28, 35}.  Farideh Firoozbakht and Jahangeer Kholdi, Nov 01 2014


LINKS



FORMULA



MATHEMATICA

f[n_] := Block[{k = 2}, While[k < 5181800 && PowerMod[n, Prime[k]  1, Prime[k]^2] != 1, k++ ]; If[k == 5181800, 0, Prime[k]]]; Table[ f[n], {n, 70}] (* Robert G. Wilson v, Jul 23 2004 *)


PROG

(PARI) for(n=2, 20, forprime(p=3, 1e9, if(Mod(n, p^2)^(p1)==1, print1(p, ", "); next({2}))); print1(", ")) \\ Felix Fröhlich, Jul 24 2014


CROSSREFS



KEYWORD

nonn,more,hard


AUTHOR



EXTENSIONS



STATUS

approved



