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Search: id:A072994
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| A072994 |
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Number of solutions to x^n==1 (mod n) 1<=x<=n. |
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+0
1
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| 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; listen)
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OFFSET
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1,4
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COMMENT
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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) for a lot of values of n except 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))
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..10000
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FORMULA
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For n>0 a(A003277(n))=1 a(2^n)=2^(n-1) a(A065119(n))=A065119(n)/3 a(A026383(n+1))=A026383(n+1)/5.
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PROGRAM
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(PARI) a(n)=(sum(i=1, n, if((i^n-1)%n, 0, 1)))
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CROSSREFS
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Sequence in context: A123317 A164879 A009195 this_sequence A052126 A094521 A159272
Adjacent sequences: A072991 A072992 A072993 this_sequence A072995 A072996 A072997
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KEYWORD
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easy,nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Aug 21 2002
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EXTENSIONS
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Corrected by T. D. Noe, May 19 2007
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