A318701 Tetrahedral numbers that are not divisible by any smaller tetrahedral number except 1.

1, 4, 10, 35, 165, 286, 969, 1771, 2925, 3654, 4495, 9139, 12341, 16215, 23426, 32509, 39711, 47905, 52394, 67525, 79079, 91881, 105995, 129766, 138415, 156849, 176851, 209934, 221815, 246905, 273819, 302621, 366145, 383306, 437989, 477191, 540274, 562475, 657359, 708561, 762355, 848046, 939929, 1004731

Offset: 1

Author

Torlach Rush, Aug 31 2018

Keywords

• nonn

Examples

			4 is a term because it is divisible by 1.
10 is a term because it is divisible by 1 but not by 4.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000292, A319788.

Programs

Maple

count:= 1: Res:= NULL:
for i from 2 while count < 100 do
  r:= i*(i+1)*(i+2)/6;
  if not ormap(t -> (r/t)::integer,[Res]) then
    Res:= Res, r;
    count:= count+1;
  fi
od:
1,Res; # Robert Israel, Dec 28 2018

Mathematica

t[n_]:=n(n+1)(n+2)/6; tQ[n_] := Module[{ans=True, tn=t[n]}, Do[If[Divisible[tn,t[i]], ans=False; Break[]],{i,2,n-1}]; ans]; t[Select[Range[100], tQ]] (* Amiram Eldar, Nov 14 2018 *)

PARI

t(n) = n*(n+1)*(n+2)/6;
isok(n) = my(tn=t(n)); for(i=2, n-1, if (!(tn % t(i)), return (0))); return (1);
lista(nn) = for (n=1, nn, if (isok(n), print1(t(n), ", "))); \\ Michel Marcus, Sep 29 2018

Extensions

a(1) = 1 inserted by Michel Marcus, Nov 09 2018