The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A072994 Number of solutions to x^n==1 (mod n), 1<=x<=n. 7
 1, 1, 1, 2, 1, 2, 1, 4, 3, 2, 1, 4, 1, 2, 1, 8, 1, 6, 1, 8, 3, 2, 1, 8, 5, 2, 9, 4, 1, 4, 1, 16, 1, 2, 1, 12, 1, 2, 3, 16, 1, 12, 1, 4, 3, 2, 1, 16, 7, 10, 1, 8, 1, 18, 5, 8, 3, 2, 1, 16, 1, 2, 9, 32, 1, 4, 1, 8, 1, 4, 1, 24, 1, 2, 5, 4, 1, 12, 1, 32, 27, 2, 1, 24, 1, 2, 1, 8, 1, 12, 1, 4, 3 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS More generally, if the equation a(x)*m=x has solutions, solutions are congruent to m: a(x)*7=x for x=7, 14, 21, 28, 49, 56, 63, 98, 112, ... . There are some composite values of m such that a(x)*m=x has solutions, as m=15. a(n) coincides with A009195(n) at many values of n, but not at n = 20, 30, 40, 42, 52, 60, 66, 68, 70, 78, 80, 84, 90, 100, ... . It seems also that for n large enough sum_{k=1..n} a(k) > n*log(n)*log(log(n)). Similar (if not the same) coincidences and differences occur between A072995 and A050399. Sequence A072989 lists these indices. - M. F. Hasler, Feb 23 2014 LINKS T. D. Noe, Table of n, a(n) for n=1..10000 FORMULA For n>0, a(A003277(n)) = 1, a(2^n) = 2^(n-1), a(A065119(n)) = A065119(n)/3. For n>1, a(A026383(n)) = A026383(n)/5. MAPLE 1, seq(nops(select(t -> t^n mod n = 1, [\$1..n-1])), n=2..100); # Robert Israel, Dec 07 2014 MATHEMATICA f[n_] := (d = If[ OddQ@ n, 1, 2]; d*Length@ Select[ Range[ n/d], PowerMod[#, n, n] == 1 &]); f[1] = f[2] = 1; Array[f, 93] (* or *) f[n_] := Length@ Select[ Range@ n, PowerMod[#, n, n] == 1 &]; f[n_] := 1 /; n<2; Array[f, 93] (* Robert G. Wilson v, Dec 06 2014 *) PROG (PARI) A072994=n->sum(k=1, n, Mod(k, n)^n==1) \\ M. F. Hasler, Feb 23 2014 CROSSREFS Sequence in context: A270120 A325567 A009195 * A332741 A052126 A094521 Adjacent sequences: A072991 A072992 A072993 * A072995 A072996 A072997 KEYWORD easy,nonn AUTHOR Benoit Cloitre, Aug 21 2002 EXTENSIONS Corrected by T. D. Noe, May 19 2007 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 6 14:43 EST 2022. Contains 358644 sequences. (Running on oeis4.)