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

1,2

Links

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

Example

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

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

Prog

(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

Crossrefs

Intersection of A000292 and A005117.

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

Sequence in context: A359317 A221907 A195269 * A126995 A271732 A219295

Adjacent sequences: A070752 A070753 A070754 * A070756 A070757 A070758

Keyword

nonn

Author

Reinhard Zumkeller, May 14 2002

Status

approved