A070755 Squarefree tetrahedral numbers.

1, 10, 35, 165, 286, 455, 969, 1330, 1771, 4495, 6545, 7770, 9139, 12341, 14190, 16215, 23426, 32509, 35990, 39711, 47905, 52394, 57155, 79079, 98770, 105995, 121485, 129766, 138415, 176851, 198485, 221815, 246905

Offset: 1

Author

Reinhard Zumkeller, May 14 2002

Keywords

• nonn

Examples

			286 = 2*11*13 is squarefree and 286 = (13*12*11)/(1*2*3) = Binomial(13,3), so 286 is a term.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Intersection of A000292 and A005117.

Cf. A000292 (tetrahedral), A005117 (squarefree), A061304 (squarefree triangular).

Programs

Maple

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

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