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A016035
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Sum phi(j), j|n, 1<=j<n. Also (for n>1) n - phi(n) - 1.
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2
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0, 0, 0, 1, 0, 3, 0, 3, 2, 5, 0, 7, 0, 7, 6, 7, 0, 11, 0, 11, 8, 11, 0, 15, 4, 13, 8, 15, 0, 21, 0, 15, 12, 17, 10, 23, 0, 19, 14, 23, 0, 29, 0, 23, 20, 23, 0, 31, 6, 29, 18, 27, 0, 35, 14, 31, 20, 29, 0, 43, 0, 31, 26, 31, 16, 45, 0, 35, 24, 45, 0, 47, 0, 37, 34, 39, 16, 53
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,6
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COMMENTS
| Number of integers less than n with at least one common factor with n. [Olivier Gerard, Feb 08 2011]
A number N is a Fermat base 2 pseudoprime, that is, 2^(N-1) == 1 mod N, iff 2^a(N) == 1 mod N. - T. D. Noe (noe(AT)sspectra.com), Jul 10 2003
Number of zero divisors in ring Z(n) - Armin Vollmer (armin_vollmer(AT)web.de), Jul 23 2004
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REFERENCES
| Al Hibbard and Ken Levasseur, "Exploring Abstract Algebra with Mathematica", Springer Verlag.
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LINKS
| Olivier Gérard, Table of n, a(n) for n = 1..9999
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EXAMPLE
| For n=6, the a(6)=3 solutions are {2,3,4}.
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MATHEMATICA
| Needs["AbstractAlgebra`Master`"] Length[ZeroDivisors[Z[ # ]]] & /@ Range[2, 25] (Vollmer)
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CROSSREFS
| Cf. A001567 (base 2 pseudoprimes).
Sequence in context: A070298 A024938 A004604 * A112470 A201582 A115379
Adjacent sequences: A016032 A016033 A016034 * A016036 A016037 A016038
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KEYWORD
| nonn,easy
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AUTHOR
| Robert G. Wilson v (rgwv(AT)rgwv.com)
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