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%I #11 Nov 22 2022 19:59:16
%S 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,
%T 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,
%U 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
%N Characteristic function of squarefree triangular integers: 1 if n(n+1)/2 is squarefree else 0.
%H Amiram Eldar, <a href="/A175608/b175608.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A008966(n(n+1)/2).
%F Asymptotic mean: lim_{n->oo} (1/n) * Sum_{k=1..n} a(k) = (3/2)*A065474 = 0.4839511484... . - _Amiram Eldar_, May 10 2022
%t Table[If[SquareFreeQ[n(n+1)/2],1,0],{n,200}]
%t If[SquareFreeQ[#],1,0]&/@Accumulate[Range[120]] (* _Harvey P. Dale_, Nov 22 2022 *)
%Y Cf. A008966 (1 if n is squarefree, else 0), A010051 (Characteristic function of primes: 1 if n is prime else 0).
%Y Cf. A000217, A061304, A065474, A215726.
%K nonn
%O 1,1
%A _Zak Seidov_, Jul 23 2010
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