A250069 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

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

LINKS

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

FORMULA

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

EXAMPLE

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

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}]

PROG

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

CROSSREFS

Cf. A006530, A014442.

Sequence in context: A160020 A273370 A273830 * A333169 A075882 A369891

Adjacent sequences: A250066 A250067 A250068 * A250070 A250071 A250072

KEYWORD

nonn,easy

AUTHOR

Michel Lagneau, Nov 11 2014

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

STATUS

approved