

A268310


Largest k > 0 such that a base b with 1 < b < c exists such that b^(c1) == 1 (mod c^k), where c is the nth composite number, or 0 if no such k exists.


4



0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0
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OFFSET

1


COMMENTS

a(n) > 0 iff c is a term of A039769.
a(n) > 1 iff c is a term of A267288. In that case, c can be called a "baseb Wieferich pseudoprime", which first happens for n = 100.
Does an integer constant t exist such that a(n) <= t for all n?


LINKS

Felix Fröhlich, Table of n, a(n) for n = 1..10000


EXAMPLE

The largest k such that c = 133, i.e. A002808(100), satisfies the congruence b^(c1) == 1 (mod c^k) for 1 < b < 133 is 2, which happens for b = 68. Since there is no other b with 1 < b < c and c satisfying this congruence for a larger k, a(100) = 2.


PROG

(PARI) forcomposite(c=1, 1e2, my(maxexp=0, k=1); for(b=2, c1, while(Mod(b, c^k)^(c1)==1, k++); if(k1 > maxexp, maxexp=k1)); print1(maxexp, ", "))


CROSSREFS

Cf. A039769, A244752, A254444, A256517, A267288.
Sequence in context: A331169 A144602 A275855 * A283316 A284508 A160351
Adjacent sequences: A268307 A268308 A268309 * A268311 A268312 A268313


KEYWORD

nonn


AUTHOR

Felix Fröhlich, Jan 31 2016


STATUS

approved



