A250069 a(n) = n^2 mod gpf(n^2 + 1) where gpf(k) is the greatest prime dividing k.

1, 4, 4, 16, 12, 36, 4, 12, 40, 100, 60, 28, 16, 196, 112, 256, 28, 12, 180, 400, 16, 96, 52, 576, 312, 676, 72, 156, 420, 52, 36, 40, 108, 88, 612, 1296, 136, 16, 760, 1600, 28, 352, 36, 148, 1012, 72, 16, 460, 1200, 60, 1300, 540, 280, 2916, 88, 3136, 12

Offset: 1

Author

Michel Lagneau, Nov 11 2014

Keywords

• nonn
• easy

Comments

For n > 1, a(n) == 0 (mod 4).

Examples

			a(5)=12 because 5^2 mod A014442(5) = 25 mod 13 = 12.
		

Links

• Michel Lagneau, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A006530, A014442.

Programs

Maple

with(numtheory):
for n from 1 to 500 do:
   p:=n^2+1:x:=factorset(p):n0:=nops(x):r:=irem(n^2,x[n0]):
   printf(`%d, `, r):
  od:

Mathematica

Table[Mod[n^2,FactorInteger[n^2+1,FactorComplete->True][[-1,1]]],{n,100}]

PARI

a(n) = lift(Mod(n, vecmax(factor(n^2+1)[,1]))^2); \\ Michel Marcus, Sep 13 2017

Formula

a(n) = n^2 mod A014442(n) where A014442(n) is the greatest prime factor of n^2 + 1.

Extensions

Edited: exchanged name with an old comment. Old name as an alternative formula. Keyword easy added. - Wolfdieter Lang, Nov 29 2014

Redundancy in Name and in Formula section removed (at the suggestion of Michel Marcus) by Jon E. Schoenfield, Sep 13 2017