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A051953
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Cototient(n) := n - phi(n).
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149
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0, 1, 1, 2, 1, 4, 1, 4, 3, 6, 1, 8, 1, 8, 7, 8, 1, 12, 1, 12, 9, 12, 1, 16, 5, 14, 9, 16, 1, 22, 1, 16, 13, 18, 11, 24, 1, 20, 15, 24, 1, 30, 1, 24, 21, 24, 1, 32, 7, 30, 19, 28, 1, 36, 15, 32, 21, 30, 1, 44, 1, 32, 27, 32, 17, 46, 1, 36, 25, 46, 1, 48, 1, 38, 35, 40, 17, 54, 1, 48, 27
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OFFSET
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1,4
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COMMENTS
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Unlike totients, cototient(n+1) = cototient(n) never holds -- except 2-phi(2) = 3 - phi(3) = 1 -- because cototient(n) is congruent to n modulo 2. - Labos E. (labos(AT)ana.sote.hu), Aug 08 2001
If n is a square-free semiprime, sopf(n) = a(n) + 1. - Wesley Ivan Hurt, May 18 2013.
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REFERENCES
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J. Browkin and A. Schinzel, On integers not of the form n-phi(n), Colloq. Math., 68 (1995), 55-58.
R. E. Jamison, The Helly bound for singular sums, Discrete Math., 249 (2002), 117-133.
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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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Equals Mobius transform (A054525) of A001065. - Gary W. Adamson, Jul 11 2008
a(n) = n - A000010(n). [From Omar E. Pol, Dec 23 2008]
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EXAMPLE
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n = 12, phi(12) = 4 = |{1, 5, 7, 11}|, a(12) = 12 - phi(12) = 8, numbers not exceeding 12 and not coprime to 12: {2, 3, 4, 6, 8, 9, 10, 12}.
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MAPLE
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with(numtheory); A051953 := n->n-phi(n);
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MATHEMATICA
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Table[n - EulerPhi[n], {n, 1, 80}] (* Carl Najafi, Aug 16 2011 *)
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PROG
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(PARI) A051953(n) = n-eulerphi(n) \\ From Michael B. Porter, Jan 28 2010
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CROSSREFS
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Cf. A000010, A005278, A001274, A098006, A054525, A001065.
Sequence in context: A112350 A063717 A024994 * A079277 A066452 A007104
Adjacent sequences: A051950 A051951 A051952 * A051954 A051955 A051956
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KEYWORD
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nonn,easy,nice,changed
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Dec 21 1999
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STATUS
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approved
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