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Search: id:A051709
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| 0, 0, 0, 1, 0, 2, 0, 3, 1, 2, 0, 8, 0, 2, 2, 7, 0, 9, 0, 10, 2, 2, 0, 20, 1, 2, 4, 12, 0, 20, 0, 15, 2, 2, 2, 31, 0, 2, 2, 26, 0, 24, 0, 16, 12, 2, 0, 44, 1, 13, 2, 18, 0, 30, 2, 32, 2, 2, 0, 64, 0, 2, 14, 31, 2, 32, 0, 22, 2, 28, 0, 75, 0, 2, 14, 24, 2, 36, 0, 58, 13, 2, 0, 80, 2, 2, 2, 44, 0
(list; graph; listen)
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OFFSET
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1,6
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COMMENT
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a(5)=sigma(5)+phi(5)-2*5 = 6+4-10 = 0.
Because sigma and phi are multiplicative functions, it is easy to show that (1) if a(n)=0, then n is prime (or 1) and (2) if a(n)=2, then n is the product of two distinct prime numbers. Note that a(n) is the n-th term of the Dirichlet series whose generating function is given below. Using the generating function, it is theoretically possible to compute a(n). Hence a(n)=0 could be used as a primarity test and a(n)=2 could be used as a test for membership in P2 (A006881). - T. D. Noe (noe(AT)sspectra.com), Aug 01 2002
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
C. Rivera, Related problem
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FORMULA
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Dirichlet g.f.: zeta(s-1) * (zeta(s) - 2 + 1/zeta(s)) - T. D. Noe (noe(AT)sspectra.com), Aug 01 2002
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CROSSREFS
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Cf. A000010, A000203, A005843, A006881, A065387, A072780.
Sequence in context: A135818 A078804 A071465 this_sequence A054656 A080096 A068915
Adjacent sequences: A051706 A051707 A051708 this_sequence A051710 A051711 A051712
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KEYWORD
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nonn
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AUTHOR
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Jud McCranie and Carlos Rivera (j.mccranie(AT)comcast.net)
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