A319788 -id:A319788 - cp's OEIS frontend

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

Torlach Rush, Aug 31 2018

nonn

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

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

Cf. A000292, A319788.

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

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 *)

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

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

A342808 Smallest k such that the k-th tetrahedral number is divisible by exactly n tetrahedral numbers.

Original entry on oeis.org

1, 2, 6, 4, 8, 28, 14, 48, 55, 98, 154, 54, 495, 1034, 504, 559, 208, 440, 2078, 2000, 350, 3519, 6578, 2574, 5983, 2924, 21734, 25023, 11934, 30303, 120175, 81718, 11438, 73150, 71630, 43470, 50048, 511784, 371448, 37960, 1478048, 391950, 812174, 393470, 217854, 576288

Offset: 1

David A. Corneth, Mar 22 2021

nonn

			a(6) = 28 as the 28th tetrahedral number, binomial(28+2, 3) = 4060, is divisible by 6 tetrahedral numbers namely 1, 4, 10, 20, 35 and 4060.

Cf. A000292, A076983, A318556, A319788.

first(n) = { my(res = vector(n), todo = n); for(i = 1, oo, c = f(i); if(c <= n && res[c] == 0, res[c] = i; todo--; if(todo <= 0, return(res)))) }
f(n) = my(d = divisors(binomial(n + 2, 3))); #select(x -> istetra(x), d) istetra(n)= my(k = sqrtnint(6*n, 3)); binomial(k + 2, 3) == n

cp's OEIS Frontend

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

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Maple

Mathematica

PARI

Extensions