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A052274 Number of distinct 5th powers mod n. 13
1, 2, 3, 3, 5, 6, 7, 5, 7, 10, 3, 9, 13, 14, 15, 9, 17, 14, 19, 15, 21, 6, 23, 15, 5, 26, 19, 21, 29, 30, 7, 17, 9, 34, 35, 21, 37, 38, 39, 25, 9, 42, 43, 9, 35, 46, 47, 27, 43, 10, 51, 39, 53, 38, 15, 35, 57, 58, 59, 45, 13, 14, 49, 34, 65, 18, 67, 51, 69, 70 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

This sequence is multiplicative. - Leon P Smith, Apr 16 2005

LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000

S. Li, On the number of elements with maximal order in the multiplicative group modulo n, Acta Arithm. 86 (2) (1998) 113, see proof of theorem 2.1

FORMULA

Conjecture: a(5^e) = 1+floor[(5-1)*5^(e+3)/(5^5-1)] if e == {0,2,3,4} (mod 5). a(5^e) = 5+floor[(5-1)*5^(e+3)/(5^5-1)] if e==1 (mod 5). - R. J. Mathar, Oct 22 2017

Conjecture: a(p^e) = 1+floor[(p-1)*p^(e+4)/{gcd(p-1,5)*(p^5-1)}] for primes p<>5  - R. J. Mathar, Oct 22 2017

MAPLE

A052274 := proc(m)

    {seq( modp(b^5, m), b=0..m-1) };

    nops(%) ;

end proc:

seq(A052274(m), m=1..100) ; # R. J. Mathar, Sep 22 2017

MATHEMATICA

With[{nn=100}, Table[Length[Union[PowerMod[Range[nn], 5, n]]], {n, nn}]] (* Harvey P. Dale, Mar 19 2016 *)

PROG

(PARI) a(n)=my(f=factor(n)); prod(i=1, #f[, 1], my(k=f[i, 1]^f[i, 2]); #vecsort(vector(k, i, i^5%k), , 8)) \\ Charles R Greathouse IV, Sep 05 2013

CROSSREFS

Cf. A000224 (squares), A046530 (cubic residues), A052273 (4th powers), A052275 (6th powers), A085310 (7th powers), A085311 (8th powers), A085312 (9th powers), A085313 (10th powers), A085314 (11th powers), A228849 (12th powers).

Sequence in context: A003967 A099209 A099208 * A085314 A085310 A055653

Adjacent sequences:  A052271 A052272 A052273 * A052275 A052276 A052277

KEYWORD

nonn,mult

AUTHOR

N. J. A. Sloane, Feb 05 2000

STATUS

approved

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Last modified January 18 11:28 EST 2019. Contains 319271 sequences. (Running on oeis4.)