A217798 Numbers n such that n^2 + 1 and (n+1)^2 + 1 are divisible by a square.

117, 407, 606, 775, 943, 1193, 1252, 1482, 1743, 1957, 2267, 2563, 3217, 3281, 3309, 3457, 3506, 3618, 3718, 3817, 4007, 4632, 4831, 5168, 5742, 5743, 5845, 6031, 6182, 6492, 6768, 7506, 7843, 8042, 8118, 8331, 8368, 8418, 8707, 8782, 8857, 9056, 9292, 9393

Offset: 1

Author

Michel Lagneau, Oct 12 2012

Keywords

• nonn

Comments

Also numbers n such that mu(n^2+1) = mu((n+1)^2+1)=0, where mu is the Moebius-function (A008683).

Examples

			117 is in the sequence because 117^2+1 = 2*5*37^2 and 118^2+1 = 5^2*557.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A002522, A068781.

Subsequence of A049532.

Programs

Magma

A002522:=func; [n: n in [1..10^4]| not IsSquarefree(A002522(n)) and not IsSquarefree(A002522(n+1))]; // Bruno Berselli, Oct 15 2012

Maple

with(numtheory):for n from 1 to 10000 do :x:=n^2+1:y:=(n+1)^2+1:if issqrfree(x)=false and issqrfree(y)=false then printf(`%d, `,n):else fi:od:

Mathematica

Select[ Range[2, 10000], Max[ Transpose[ FactorInteger[ #^2+1 ]] [[2]]] > 1 && Max[ Transpose[ FactorInteger[ (#+1)^2 + 1]] [[2]]] > 1 &]