

A052273


Number of distinct 4th powers mod n.


14



1, 2, 2, 2, 2, 4, 4, 2, 4, 4, 6, 4, 4, 8, 4, 2, 5, 8, 10, 4, 8, 12, 12, 4, 6, 8, 10, 8, 8, 8, 16, 4, 12, 10, 8, 8, 10, 20, 8, 4, 11, 16, 22, 12, 8, 24, 24, 4, 22, 12, 10, 8, 14, 20, 12, 8, 20, 16, 30, 8, 16, 32, 16, 6, 8, 24, 34, 10, 24, 16, 36, 8, 19, 20, 12, 20
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OFFSET

1,2


COMMENTS

This sequence is multiplicative [Li].  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(2^e) = 1+floor[2^e/(2^41)] if e ==0 (mod 4). a(2^e) = 2+floor[2^e/(2^41)] if e == {1,2,3} mod 4.  R. J. Mathar, Oct 22 2017
Conjecture: a(p^e) = 1+floor[ (p1)*p^(e+3)/{gcd(p1,4)*(p^41)}] for odd primes p.  R. J. Mathar, Oct 22 2017


MAPLE

A052273 := proc(n, k) local i; nops({seq(i^k mod n, i=0..n1)}); end; # number of kth powers mod n


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^4%k), , 8)) \\ Charles R Greathouse IV, May 26 2013


CROSSREFS

Cf. A000224 (squares), A046530 (cubic residues), A052274 (5th 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: A023155 A277847 A085311 * A074912 A274207 A158502
Adjacent sequences: A052270 A052271 A052272 * A052274 A052275 A052276


KEYWORD

nonn,mult


AUTHOR

N. J. A. Sloane, Feb 05 2000


STATUS

approved



