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Search: id:A063994
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| A063994 |
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Product_{primes p dividing n } GCD(p-1, n-1). |
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+0
2
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| 1, 1, 2, 1, 4, 1, 6, 1, 2, 1, 10, 1, 12, 1, 4, 1, 16, 1, 18, 1, 4, 1, 22, 1, 4, 1, 2, 3, 28, 1, 30, 1, 4, 1, 4, 1, 36, 1, 4, 1, 40, 1, 42, 1, 8, 1, 46, 1, 6, 1, 4, 3, 52, 1, 4, 1, 4, 1, 58, 1, 60, 1, 4, 1, 16, 5, 66, 1, 4, 3, 70, 1, 72, 1, 4, 3, 4, 1, 78, 1, 2, 1, 82, 1, 16, 1, 4, 1, 88, 1, 36, 1
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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a(n) = number of bases b mod n for which b^{n-1} = 1 mod n.
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REFERENCES
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Baillie and Wagstaff, Mathematics of Computation, 35 (1980), 1391-1417.
P. Erdos and C. Pomerance, Mathematics of Computation, 46 (1986), 259-279.
Keith Gibson, posting to Number Theory List, Sep 07, 2001.
Carl Pomerance, posting to Number Theory List, Sep 07, 2001.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
W. R. Alford, A. Granville and C. Pomerance, There are infinitely many Carmichael numbers, Ann. of Math. (2) 139 (1994), no. 3, 703-722.
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MATHEMATICA
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f[n_ ] := If[n == 1, 1, Apply[ Times, GCD[n - 1, Transpose[ FactorInteger[n]] [[1]] - 1]]]; Table[f[n], {n, 1, 100} ]
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PROGRAM
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(PARI) { for (n=1, 1000, f=factor(n)~; a=1; for (i=1, length(f), a*=gcd(f[1, i] - 1, n - 1)); write("b063994.txt", n, " ", a) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Sep 05 2009]
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CROSSREFS
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Cf. A002997.
Sequence in context: A060680 A057237 A049559 this_sequence A076512 A128707 A161510
Adjacent sequences: A063991 A063992 A063993 this_sequence A063995 A063996 A063997
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Sep 18 2001
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 21 2001
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