A333923 a(n) is the smallest positive integer such that n^a(n) is divisible by n+a(n).

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, 54, 4, 812, 6, 930, 32, 48, 30, 14, 12, 1332, 26, 42, 10, 1640, 6, 1806, 20, 30, 18, 2162, 6, 294, 14, 30, 12, 2756, 10, 66, 8, 24, 6, 3422, 4, 3660, 62, 18, 64, 60, 6, 4422

Offset: 2

Author

Scott R. Shannon, Apr 10 2020

Keywords

• nonn

Comments

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.

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.

Examples

			a(2) = 2 as 2 ^ 2 = 4 is divisible by 2 + 2 = 4.
a(3) = 6 as 3 ^ 6 = 729 is divisible by 3 + 6 = 9.
a(4) = 4 as 4 ^ 4 = 256 is divisible by 4 + 4 = 8.
a(5) = 20 as 5 ^ 20 = 95367431640625 is divisible by 5 + 20 = 25.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 2..1000

Crossrefs

Cf. A063427, A333811, A332795, A332703.

Programs

Mathematica

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