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 A006511 Largest inverse of totient function (A000010): a(n) is the largest x such that phi(x)=m, where m=A002202(n) is the n-th number in the range of phi. (Formerly M1580) 20
 2, 6, 12, 18, 30, 22, 42, 60, 54, 66, 46, 90, 58, 62, 120, 126, 150, 98, 138, 94, 210, 106, 162, 174, 118, 198, 240, 134, 142, 270, 158, 330, 166, 294, 276, 282, 420, 250, 206, 318, 214, 378, 242, 348, 354, 462, 254, 510, 262, 414, 274, 278, 426, 630, 298, 302 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Always even, as phi(2n)=phi(n) when n is odd. - Alain Jacques (thegentleway(AT)bigpond.com), Jun 15 2006 REFERENCES J. W. L. Glaisher, Number-Divisor Tables. British Assoc. Math. Tables, Vol. 8, Camb. Univ. Press, 1940, p. 64. N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS T. D. Noe, Table of n, a(n) for n=1..10000 R. K. Guy, Letter to N. J. A. Sloane, Jun 1991 FORMULA a(n) = A057635(A002202(n)). - T. D. Noe MATHEMATICA phiinv[n_, pl_] := Module[{i, p, e, pe, val}, If[pl=={}, Return[If[n==1, {1}, {}]]]; val={}; p=Last[pl]; For[e=0; pe=1, e==0||Mod[n, (p-1)pe/p]==0, e++; pe*=p, val=Join[val, pe*phiinv[If[e==0, n, n*p/pe/(p-1)], Drop[pl, -1]]]]; Sort[val]]; phiinv[n_] := phiinv[n, Select[1+Divisors[n], PrimeQ]]; Last/@Select[phiinv/@Range[1, 200], #!={}&] (* phiinv[n, pl] = list of x with phi(x)=n and all prime divisors of x in list pl. phiinv[n] = list of x with phi(x)=n *) PROG (Perl) use ntheory ":all"; my \$k=1; for my \$i (1..100) { my @v; do{@v=inverse_totient(\$k++)} until @v; print "\$i \$v[-1]\n"; } # Dana Jacobsen, Mar 04 2019 (PARI) g(n) = if(n%2, 2*(n==1), forstep(k = floor(exp(Euler)*n*log(log(n^2))+2.5*n/log(log(n^2))), n, -1, if(eulerphi(k)==n, return(k)); if(k==n, return(0)))); \\ A057635 lista(nn) = for(m = 1, nn, if(istotient(m), print1(g(m), ", "))); \\ Jinyuan Wang, Aug 29 2019 CROSSREFS Cf. A000010, A002202, A002181, A057826. For records see A036913, A132154, A036912. Sequence in context: A278484 A159793 A238739 * A325708 A113274 A181660 Adjacent sequences: A006508 A006509 A006510 * A006512 A006513 A006514 KEYWORD nonn AUTHOR N. J. A. Sloane STATUS approved

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Last modified February 26 09:41 EST 2024. Contains 370338 sequences. (Running on oeis4.)