A066069 -id:A066069 - cp's OEIS frontend

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

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

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

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

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

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 *)

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

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

A066070 a(1) = 1; for m > 0, a(2m) = 2(2m+1), a(2m+1) = 2m+1.

Original entry on oeis.org

1, 6, 3, 10, 5, 14, 7, 18, 9, 22, 11, 26, 13, 30, 15, 34, 17, 38, 19, 42, 21, 46, 23, 50, 25, 54, 27, 58, 29, 62, 31, 66, 33, 70, 35, 74, 37, 78, 39, 82, 41, 86, 43, 90, 45, 94, 47, 98, 49, 102, 51, 106, 53, 110, 55, 114, 57, 118, 59, 122, 61, 126, 63, 130, 65, 134, 67, 138

Offset: 1

George E. Antoniou, Dec 02 2001

Harry J. Smith, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1).

Cf. A066069.

LinearRecurrence[{0,2,0,-1},{1,6,3,10},70] (* Harvey P. Dale, Jan 13 2022 *)

{ for (n=1, 1000, a=if (n%2, n, 2*n + 2); write("b066070.txt", n, " ", a) ) } \\ Harry J. Smith, Nov 09 2009

O.g.f.: (x+6x^2+x^3-2x^4)/(1-x^2)^2. - Len Smiley, Dec 05 2001

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

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A066070 a(1) = 1; for m > 0, a(2m) = 2(2m+1), a(2m+1) = 2m+1.

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