A019530 Smallest number m such that m^m is divisible by n.

0, 2, 3, 2, 5, 6, 7, 4, 3, 10, 11, 6, 13, 14, 15, 4, 17, 6, 19, 10, 21, 22, 23, 6, 5, 26, 3, 14, 29, 30, 31, 4, 33, 34, 35, 6, 37, 38, 39, 10, 41, 42, 43, 22, 15, 46, 47, 6, 7, 10, 51, 26, 53, 6, 55, 14, 57, 58, 59, 30, 61, 62, 21, 4, 65, 66, 67, 34, 69, 70, 71, 6, 73, 74, 15, 38, 77, 78

Offset: 1

Author

D. Muller (Research37(AT)aol.com)

Keywords

• nonn
• easy

Comments

Numbers n such that a(n) = n are 2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 26, 29, 30, 31, 33, 34, 35, 37, 38, 39, 41, 42, 43, 46, 47, 51, 53, 55, 57, 58, 59, 61, 62, 65, 66, 67, 69, 70, ... (A144338). - Altug Alkan, Sep 30 2016

For n > 1, a(n) = A007947(n) * k for some k. Mostly, k = 1. - David A. Corneth, Sep 30 2016

For n > 1, a(n) = A007947(n) if and only if A007947(n) >= A051903(n). - Robert Israel, Sep 30 2016

Links

• Altug Alkan, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000312, A007947, A051903, A066069, A144338, A277128.

Programs

Mathematica

a[1] = 0; a[n_] := For[m = 2, True, m++, If[PowerMod[m, m, n] == 0, Return[m]]]; Array[a, 100] (* Jean-François Alcover, Sep 30 2016 *)
snm[n_]:=Module[{m=1},While[PowerMod[m,m,n]!=0,m++];m]; Join[{0},Array[snm,100,2]] (* Harvey P. Dale, Mar 14 2025 *)

PARI

a(n)={my(f=factor(n)[,1], p=prod(i=1, #f, f[i]), i=1); if(n==1,return(0)); while(1, if(Mod(p*i,n)^(p*i)==0, return(p*i) ,i++))} \\ David A. Corneth, Sep 30 2016

PARI

a(n)=if(n<=1,return(0)); for(m=2,n,if(Mod(m,n)^m==0,return(m))); \\ Joerg Arndt, Oct 01 2016