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A053578
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Values of cototient function for A053577.
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2
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1, 1, 2, 1, 4, 1, 4, 1, 8, 1, 8, 8, 1, 1, 1, 16, 16, 1, 1, 16, 1, 1, 1, 1, 32, 1, 32, 1, 1, 32, 32, 1, 1, 1, 1, 1, 1, 64, 1, 1, 1, 1, 1, 64, 1, 64, 1, 64, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 128, 1, 1, 1, 1, 1, 128, 1, 1, 1, 1, 1, 128, 1, 128, 128, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
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OFFSET
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1,3
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COMMENTS
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Except for 2^0 = 1, there are only finitely many values of k such that cototient(k) = 2^m for fixed m.
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LINKS
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EXAMPLE
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For p prime, cototient(p) = 1. Smallest values for which cototient(x) = 2^w are A058764(w) = A007283(w-1) = 3*2^(w-1) = 6, 12, 24, 48, 96, 192, .., 49152 for w = 2, 3, 4, 5, 6, ..., 15. [Corrected by M. F. Hasler, Nov 10 2016]
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MATHEMATICA
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Select[Table[k - EulerPhi[k], {k, 1, 400}], # == 2^IntegerExponent[#, 2] &] (* Amiram Eldar, Jun 09 2024 *)
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PROG
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(PARI) lista(kmax) = {my(c); for(k = 2, kmax, c = k - eulerphi(k); if(c >> valuation(c, 2) == 1, print1(c, ", "))); } \\ Amiram Eldar, Jun 09 2024
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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