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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 October 15 10:15 EDT 2019. Contains 328026 sequences. (Running on oeis4.)