

A319484


a(n) is the smallest k > 1 such that n^k == n (mod k) and gcd(k, b^kb) = 1 for some b <> n.


0



35, 35, 7957, 16531, 1247, 4495, 35, 817, 2501, 697, 55, 55, 143, 221, 35, 35, 1247, 493, 221, 95, 35, 35, 77, 253, 115, 403, 247, 247, 203, 35, 155, 155, 697, 187, 35, 35, 35, 589, 221, 95, 533, 35, 287, 77, 55, 55, 115, 221, 329, 35, 35, 221, 221, 689, 55, 35, 35
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OFFSET

0,1


COMMENTS

a(n) is the smallest k > 1 such that n^k == n (mod k) and p1 does not divide k1 for every prime p dividing k, see A121707.
It seems that the sequence is unbounded like A316940.
The term a(5) = 4495 = 5*29*31 is not semiprime.


LINKS



EXAMPLE

a(6) = 35 since 6^35 == 6 (mod 35) and 35 = 5*7 is the smallest "antiCarmichael number": 51 does not divide 71. We have gcd(35,2^352) = 1.


PROG

(PARI) isac(n) = {my(f = factor(n)[, 1]); for (i=1, #f, if (((n1) % (f[i]1)) == 0, return (0)); ); return (1); }
isok(n, k) = {if (Mod(n, k)^k != Mod(n, k), return (0)); return (isac(k)); }
a(n) = {my(k=2); while (!isok(n, k), k++); return (k); } \\ Michel Marcus, Oct 27 2018


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



