A049283 - OEIS

A049283

a(n) is the smallest k such that phi(k) = n, where phi is Euler's totient function, or a(n) = 0 if no such k exists.

1, 3, 0, 5, 0, 7, 0, 15, 0, 11, 0, 13, 0, 0, 0, 17, 0, 19, 0, 25, 0, 23, 0, 35, 0, 0, 0, 29, 0, 31, 0, 51, 0, 0, 0, 37, 0, 0, 0, 41, 0, 43, 0, 69, 0, 47, 0, 65, 0, 0, 0, 53, 0, 81, 0, 87, 0, 59, 0, 61, 0, 0, 0, 85, 0, 67, 0, 0, 0, 71, 0, 73, 0, 0, 0, 0, 0, 79, 0, 123, 0, 83, 0, 129, 0, 0, 0, 89

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

T. D. Noe, Table of n, a(n) for n = 1..10000

Max Alekseyev, PARI/GP Scripts for Miscellaneous Math Problems (invphi.gp).

EXAMPLE

The smallest k such that phi(k) = 2 is k = 3, so a(2) = 3.

MATHEMATICA

Module[{nn=140, ep}, ep=Table[{k, EulerPhi[k]}, {k, 0, nn}]; Table[SelectFirst[ep, #[[2]]==n&], {n, nn}]][[;; , 1]]/."NotFound"->0 (* Harvey P. Dale, Jul 29 2023 *)

PROG

(PARI) a(n)=if(n>2, for(k=n+1, solve(x=n, 2*n^2, x/(exp(Euler)*log(log(x))+3/log(log(x)))-n), if(eulerphi(k)==n, return(k))); 0, 2*n-1) \\ Charles R Greathouse IV, Nov 28 2012

(PARI) x=1000; v=vector(x\(exp(Euler)*log(log(x))+3/log(log(x)))); for(n=1, x, t=eulerphi(n); if(t<=#v && !v[t], v[t]=n)); v \\ Charles R Greathouse IV, Nov 28 2012

(PARI) a(n) = max(0, invphiMin(n)); \\ Amiram Eldar, Nov 15 2024, using Max Alekseyev's invphi.gp

CROSSREFS

Cf. A000010, A014197, A057635.

Sequence in context: A352505 A210524 A325961 * A141162 A160035 A281648

Adjacent sequences: A049280 A049281 A049282 * A049284 A049285 A049286

KEYWORD

nonn,changed

AUTHOR

Jud McCranie, Oct 10 2000

STATUS

approved