A175608 Characteristic function of squarefree triangular integers: 1 if n(n+1)/2 is squarefree else 0.

1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1

Offset: 1

Author

Zak Seidov, Jul 23 2010

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A008966 (1 if n is squarefree, else 0), A010051 (Characteristic function of primes: 1 if n is prime else 0).

Cf. A000217, A061304, A065474, A215726.

Programs

Mathematica

Table[If[SquareFreeQ[n(n+1)/2],1,0],{n,200}]
If[SquareFreeQ[#],1,0]&/@Accumulate[Range[120]] (* Harvey P. Dale, Nov 22 2022 *)

Formula

a(n) = A008966(n(n+1)/2).

Asymptotic mean: lim_{n->oo} (1/n) * Sum_{k=1..n} a(k) = (3/2)*A065474 = 0.4839511484... . - Amiram Eldar, May 10 2022