

A065295


Number of values of s, 0 < s <= n1, such that s^s == s (mod n).


6



0, 1, 1, 2, 1, 4, 2, 4, 3, 4, 1, 7, 2, 5, 7, 6, 3, 8, 2, 9, 7, 5, 2, 13, 5, 8, 3, 11, 2, 14, 3, 6, 8, 8, 9, 13, 2, 7, 9, 17, 5, 18, 3, 11, 13, 5, 2, 19, 9, 12, 11, 13, 1, 8, 11, 18, 9, 7, 1, 27, 4, 7, 20, 10, 16, 18, 3, 13, 8, 21, 2, 23, 5, 6, 16, 14, 13, 23, 4, 27, 9, 11, 1, 31, 13, 10, 12, 20
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OFFSET

1,4


COMMENTS

Note that a(1) = 0 by definition.  Harry J. Smith, Oct 15 2009


LINKS

Harry J. Smith and T. D. Noe, Table of n, a(n) for n = 1..10000 (first 1000 terms from Harry J. Smith)


EXAMPLE

For n=5 we have (1^1) mod 5 = 1, (2^2) mod 5 = 4, (3^3) mod 5 = 2, (4^4) mod 5 = 1. Only for s=1 does (s^s) mod 5=s, so a(5)=1


MATHEMATICA

f[p_] := Module[{x = Range[p1]}, Count[PowerMod[x, x, p]  x, 0]]; Table[f[n], {n, 100}] (* T. D. Noe, Feb 19 2014 *)


PROG

(PARI) { for (n=1, 1000, a=0; for (s=1, n  1, if (s^s % n == s, a++)); if (n==1, a=0); write("b065295.txt", n, " ", a) ) } [Harry J. Smith, Oct 15 2009]


CROSSREFS

Cf. A065296.
Sequence in context: A321088 A070556 A277687 * A296604 A261211 A233521
Adjacent sequences: A065292 A065293 A065294 * A065296 A065297 A065298


KEYWORD

nonn


AUTHOR

Jonathan Ayres (jonathan.ayres(AT)btinternet.com), Oct 28 2001


EXTENSIONS

Definition revised by N. J. A. Sloane, Oct 15 2009.


STATUS

approved



