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

1,1

Links

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

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

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 *)

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.

Sequence in context: A144778 A143142 A174856 * A285467 A194679 A111940

Adjacent sequences: A175605 A175606 A175607 * A175609 A175610 A175611

Keyword

nonn

Author

Zak Seidov, Jul 23 2010

Status

approved