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A070755 Squarefree tetrahedral numbers. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A240267 A221907 A195269 * A126995 A271732 A219295

Adjacent sequences:  A070752 A070753 A070754 * A070756 A070757 A070758

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, May 14 2002

STATUS

approved

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Last modified September 21 07:28 EDT 2021. Contains 347596 sequences. (Running on oeis4.)