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
Offset: 1
Keywords
Examples
The smallest k such that phi(k) = 2 is k = 3, so a(2) = 3.
Links
- T. D. Noe, Table of n, a(n) for n = 1..10000
- Max Alekseyev, PARI/GP Scripts for Miscellaneous Math Problems (invphi.gp).
Programs
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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 *) -
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
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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
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PARI
a(n) = max(0, invphiMin(n)); \\ Amiram Eldar, Nov 15 2024, using Max Alekseyev's invphi.gp