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A063752
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Numbers k such that cototient(k) is a square.
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12
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1, 2, 3, 5, 6, 7, 8, 11, 13, 17, 19, 21, 23, 24, 27, 28, 29, 31, 32, 37, 41, 43, 47, 53, 54, 59, 61, 67, 68, 69, 71, 73, 79, 83, 89, 96, 97, 101, 103, 107, 109, 112, 113, 124, 125, 127, 128, 131, 133, 137, 139, 141, 149, 151, 157, 163, 167, 173, 179, 181, 189, 191
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OFFSET
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1,2
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COMMENTS
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Some different families and subsequences of integers belong to this sequence, see the file "Subfamilies and subsequences" for more details, with data, comments, proofs, formulas and examples. - Bernard Schott, Mar 05 2019
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LINKS
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Thomas E. Moore, Problem 1204, Crux Mathematicorum, page 93, Vol. 14, Mar. 88.
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FORMULA
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a(n) seems to be asymptotic to c * n * log(n) with c = 1.7... (all primes are in the sequence since cototient(p) = 1). - Benoit Cloitre, Sep 08 2002
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MATHEMATICA
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PROG
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(PARI) j=[]; for(n=1, 400, x=n-eulerphi(n); if(issquare(x), j=concat(j, n))); j
(PARI) { n=0; for (m=1, 10^9, if (issquare(m - eulerphi(m)), write("b063752.txt", n++, " ", m); if (n==1000, break)) ) } \\ Harry J. Smith, Aug 29 2009
(Magma) [n: n in [1..200] | IsSquare(n - EulerPhi(n))]; // Vincenzo Librandi, Jan 11 2019
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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