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

%I A019530 #43 Mar 14 2025 18:40:00
%S A019530 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,
%T A019530 29,30,31,4,33,34,35,6,37,38,39,10,41,42,43,22,15,46,47,6,7,10,51,26,
%U A019530 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
%N A019530 Smallest number m such that m^m is divisible by n.
%C A019530 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
%C A019530 For n > 1, a(n) = A007947(n) * k for some k. Mostly, k = 1. - _David A. Corneth_, Sep 30 2016
%C A019530 For n > 1, a(n) = A007947(n) if and only if A007947(n) >= A051903(n). - _Robert Israel_, Sep 30 2016
%H A019530 Altug Alkan, <a href="/A019530/b019530.txt">Table of n, a(n) for n = 1..10000</a>
%t A019530 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 *)
%t A019530 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 *)
%o A019530 (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
%o A019530 (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
%Y A019530 Cf. A000312, A007947, A051903, A066069, A144338, A277128.
%K A019530 nonn,easy
%O A019530 1,2
%A A019530 D. Muller (Research37(AT)aol.com)