A272101 Square root of largest square dividing A069482(n).

1, 4, 2, 6, 4, 2, 6, 2, 2, 2, 2, 2, 2, 6, 10, 4, 4, 16, 2, 12, 4, 18, 2, 4, 6, 2, 2, 12, 2, 4, 2, 2, 2, 24, 10, 2, 8, 2, 2, 8, 12, 2, 16, 2, 6, 2, 2, 30, 4, 2, 4, 8, 2, 2, 4, 2, 6, 2, 6, 2, 24, 20, 2, 4, 6, 36, 2, 6, 4, 6

Offset: 1

Author

Benedict W. J. Irwin, Apr 20 2016

Keywords

• nonn

Comments

Analogous to A001223 with 2-norm.

a(n) is the square root of the square part of A069482(n).

Examples

			sqrt(5)=1*sqrt(5), a(n)=1.
sqrt(16)=4*sqrt(1), a(n)=4.
sqrt(24)=2*sqrt(6), a(n)=2.
		

Crossrefs

Cf. A000188, A069482

Cf. A001223, A068361.

Programs

Mathematica

Table[Sqrt[Prime[n+1]^2-Prime[n]^2],{n,1,100}]/.Sqrt[_]->1

PARI

a(n) = my(d=prime(n+1)^2 - prime(n)^2); sqrtint(d/core(d)); \\ Michel Marcus, Apr 27 2016

Formula

Conjectures: (Start)

a(A068361(n)) = A001223(A068361(n)).

a(A068361(n)) = 2 for n>1.

These are the only a(n)=A001223(n).

(End)

a(n) = A000188(A069482(n)). - Michel Marcus, Apr 27 2016