A318701 -id:A318701 - cp's OEIS frontend

A319788 Tetrahedral numbers divisible by a record number of smaller tetrahedral numbers.

1, 4, 20, 120, 560, 19600, 27720, 1521520, 7207200, 2845642800, 4170866700, 249466897680, 9117204216120, 1723262134513920, 2525472914524560, 189169152233901840, 1782424363173854400, 28708458878287188000, 15137401000857582807360, 32632841312905676442600, 647550654467707884653760

Offset: 1

Torlach Rush, Sep 27 2018

nonn

For known terms > 1:
- a(n) is divisible by a square.
- a(n) is divisible by 20, n > 2.
The record numbers of tetrahedral divisors corresponding to terms a(1)-a(21) are 0, 1, 3, 4, 6, 7, 11, 16, 20, 23, 25, 32, 39, 44, 53, 57, 58, 64, 69, 72, 84.
a(18)..a(21) are divisible by 25878772920. If a(22)..a(28) are divisible by 25878772920 then they are binomial(k + 2, 3) for k in {879207614, 4118478208, 6399801198, 8921309759, 9985690350, 14992913375} having 94, 96, 98, 101, 106, 118 smaller tetrahedral divisors respectively. - David A. Corneth, Mar 22 2021

			4 is a term because it is the smallest tetrahedral number divisible by the only positive smaller tetrahedral number 1.
20 is a term because it divisible by 1,4,10, and has more divisors than each of 1,4,10, the only smaller terms.

Cf. A000292, A084260, A318556, A318701.

Subsequence of A013929.

t(n) = n*(n+1)*(n+2)/6;
f(n) = my(tn=n*(n+1)*(n+2)/6); sum(k=1, n-1, (tn % t(k)) == 0);
lista(nn) = {my(nb = - 1, new); for (n=1, nn, new = f(n); if (new > nb, print1(t(n), ", "); nb = new););} \\ Michel Marcus, Oct 02 2018

a(17)-a(18) from Giovanni Resta, Sep 28 2018

a(19)-a(21) from Bert Dobbelaere, Mar 21 2021

cp's OEIS Frontend

A319788 Tetrahedral numbers divisible by a record number of smaller tetrahedral numbers.

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