A264665 Integers n such that A002110(n) + 2 is the sum of 2 nonzero squares.

2, 3, 4, 5, 6, 11, 15, 33, 49, 50, 52, 53, 54, 57, 60, 61, 64, 68

Offset: 1

Author

Altug Alkan, Nov 20 2015

Keywords

• nonn
• more

Comments

Integers n such that A006862(n) + 1 is the sum of 2 nonzero squares.

Examples

			a(1) = 2 because 2*3 + 2 = 2^2 + 2^2.
a(2) = 3 because 2*3*5 + 2 = 4^2 + 4^2.
a(3) = 4 because 2*3*5*7 + 2 = 14^2 + 4^2.
		

Crossrefs

Cf. A000404, A002110, A006862.

Programs

Mathematica

Rest@ Select[Range@ 36, SquaresR[2, Product[Prime@ k, {k, #}] + 2] > 0 &] (* Michael De Vlieger, Nov 23 2015 *)

PARI

a(n) = prod(k=1, n, prime(k)) + 2;
is(n) = { for( i=1, #n=factor(n)~%4, n[1, i]==3 && n[2, i]%2 && return); n && ( vecmin(n[1, ])==1 || (n[1, 1]==2 && n[2, 1]%2)) }
for(n=1, 1e5, if(is(a(n)), print1(n, ", ")))