A333923 - OEIS

%I #20 Jan 16 2022 16:17:32

%S 2,6,4,20,3,42,8,18,6,110,4,156,14,10,16,272,6,342,5,6,10,506,3,100,6,

%T 54,4,812,6,930,32,48,30,14,12,1332,26,42,10,1640,6,1806,20,30,18,

%U 2162,6,294,14,30,12,2756,10,66,8,24,6,3422,4,3660,62,18,64,60,6,4422

%N a(n) is the smallest positive integer such that n^a(n) is divisible by n+a(n).

%C As in A063427, if n is a prime then a(n^k) = (n-1)*n^k for k>=1. This sequence also matches A063427 for numerous other nonprime terms for small values of n.

%C For n below 10000 the values where n = a(n), other than n being a power of 2, are n = 14, 62, 122, 254, 508, 1018, 2038, 2042, 8182, 8186.

%H Harvey P. Dale, <a href="/A333923/b333923.txt">Table of n, a(n) for n = 2..1000</a>

%e a(2) = 2 as 2 ^ 2 = 4 is divisible by 2 + 2 = 4.

%e a(3) = 6 as 3 ^ 6 = 729 is divisible by 3 + 6 = 9.

%e a(4) = 4 as 4 ^ 4 = 256 is divisible by 4 + 4 = 8.

%e a(5) = 20 as 5 ^ 20 = 95367431640625 is divisible by 5 + 20 = 25.

%t spi[n_]:=Module[{k=1},While[PowerMod[n,k,n+k]!=0,k++];k]; Array[spi,70,2] (* _Harvey P. Dale_, Jan 16 2022 *)

%Y Cf. A063427, A333811, A332795, A332703.

%K nonn

%O 2,1

%A _Scott R. Shannon_, Apr 10 2020