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%I #18 Feb 22 2017 15:50:05
%S 1,10,35,165,286,455,969,1330,1771,4495,6545,7770,9139,12341,14190,
%T 16215,23426,32509,35990,39711,47905,52394,57155,79079,98770,105995,
%U 121485,129766,138415,176851,198485,221815,246905
%N Squarefree tetrahedral numbers.
%H Charles R Greathouse IV, <a href="/A070755/b070755.txt">Table of n, a(n) for n = 1..10000</a>
%e 286 = 2*11*13 is squarefree and 286 = (13*12*11)/(1*2*3) = Binomial(13,3), so 286 is a term.
%p with(numtheory): A070755:=n->`if`(mobius(n*(n+1)*(n+2)/6)^2=1,n*(n+1)*(n+2)/6,NULL): seq(A070755(n), n=1..100); # _Wesley Ivan Hurt_, Oct 10 2014
%o (PARI) list(lim)=my(v=List(),t); forstep(n=1,sqrtnint(lim\1*6,3),[2,2,4], if(issquarefree(n/gcd(n,6)) && issquarefree((n+1)/gcd(n+1,6)) && issquarefree((n+2)/gcd(n+2,6)) && (t=binomial(n+2,3))<=lim, listput(v,t))); Vec(v) \\ _Charles R Greathouse IV_, Feb 22 2017
%Y Intersection of A000292 and A005117.
%Y Cf. A000292 (tetrahedral), A005117 (squarefree), A061304 (squarefree triangular).
%K nonn
%O 1,2
%A _Reinhard Zumkeller_, May 14 2002
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