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A319048
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a(n) is the greatest k such that A000010(k) divides n where A000010 is the Euler totient function.
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3
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2, 6, 2, 12, 2, 18, 2, 30, 2, 22, 2, 42, 2, 6, 2, 60, 2, 54, 2, 66, 2, 46, 2, 90, 2, 6, 2, 58, 2, 62, 2, 120, 2, 6, 2, 126, 2, 6, 2, 150, 2, 98, 2, 138, 2, 94, 2, 210, 2, 22, 2, 106, 2, 162, 2, 174, 2, 118, 2, 198, 2, 6, 2, 240, 2, 134, 2, 12, 2, 142, 2, 270, 2, 6, 2, 12, 2, 158, 2, 330
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OFFSET
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1,1
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COMMENTS
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Sandor calls this function the totient maximum function and remarks that this function is well-defined, since a(n) can be at least 2, and cannot be greater than n^2 (when n > 6).
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LINKS
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FORMULA
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MATHEMATICA
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a[n_] := Module[{kmax = If[n <= 6, 10 n, n^2]}, For[k = kmax, True, k--, If[Divisible[n, EulerPhi[k]], Return[k]]]];
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PROG
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(PARI) a(n) = {my(kmax = if (n<=6, 10*n, n^2)); forstep (k=kmax, 1, -1, if ((n % eulerphi(k)) == 0, return (k)); ); }
(PARI)
\\ (The first two functions could probably be combined in a smarter way):
A014197(n, m=1) = { n==1 && return(1+(m<2)); my(p, q); sumdiv(n, d, if( d>=m && isprime(d+1), sum( i=0, valuation(q=n\d, p=d+1), A014197(q\p^i, p))))} \\ From A014197 by M. F. Hasler
A057635(n) = if(1==n, 2, if((n%2), 0, my(k=A014197(n), i=n); if(!k, 0, while(k, i++; if(eulerphi(i)==n, k--)); (i))));
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CROSSREFS
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Cf. A319068 (the analog for the sum of divisors).
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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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