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%I #47 Mar 23 2021 15:52:03
%S 1,4,20,120,560,19600,27720,1521520,7207200,2845642800,4170866700,
%T 249466897680,9117204216120,1723262134513920,2525472914524560,
%U 189169152233901840,1782424363173854400,28708458878287188000,15137401000857582807360,32632841312905676442600,647550654467707884653760
%N Tetrahedral numbers divisible by a record number of smaller tetrahedral numbers.
%C For known terms > 1:
%C - a(n) is divisible by a square.
%C - a(n) is divisible by 20, n > 2.
%C 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.
%C 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
%e 4 is a term because it is the smallest tetrahedral number divisible by the only positive smaller tetrahedral number 1.
%e 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.
%o (PARI) t(n) = n*(n+1)*(n+2)/6;
%o f(n) = my(tn=n*(n+1)*(n+2)/6); sum(k=1, n-1, (tn % t(k)) == 0);
%o 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
%Y Cf. A000292, A084260, A318556, A318701.
%Y Subsequence of A013929.
%K nonn
%O 1,2
%A _Torlach Rush_, Sep 27 2018
%E a(17)-a(18) from _Giovanni Resta_, Sep 28 2018
%E a(19)-a(21) from _Bert Dobbelaere_, Mar 21 2021
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