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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
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
For records see A036913, A132154, A036912.
Sequence in context: A278484 A159793 A238739 * A325708 A113274 A181660
KEYWORD
nonn
AUTHOR
STATUS
approved

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