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

1,2

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A277803 A062789 A066069 * A355263 A019554 A371573

Adjacent sequences: A019527 A019528 A019529 * A019531 A019532 A019533

Keyword

nonn,easy

Author

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

Status

approved