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A318556 a(n) is the number of lesser tetrahedral numbers that divide the n-th tetrahedral number.

%I A318556 #21 Mar 23 2021 15:51:44
%S A318556 0,1,1,3,1,2,2,4,1,4,1,2,2,6,4,2,1,4,3,6,1,2,4,4,1,4,1,5,1,4,2,2,2,6,
%T A318556 3,2,1,4,4,6,1,2,3,6,1,2,3,7,2,4,1,2,2,11,8,3,1,4,2,4,1,4,11,6,1,2,1,
%U A318556 5,2,8,2,2,1,4,4,4,1,4,5,5,1,2,3,5,1,2,2,7,3,8,1,2,1,4,4,3,1,9
%N A318556 a(n) is the number of lesser tetrahedral numbers that divide the n-th tetrahedral number.
%H A318556 David A. Corneth, <a href="/A318556/b318556.txt">Table of n, a(n) for n = 1..10000</a>
%F A318556 a(n) = Sum_{m=1..n-1} [0 = A000292(n) mod A000292(m)]. Here [] is the Iverson bracket function.
%e A318556 t(4) is 20 and 20 is divisible by t(1)=1, t(2)=4 and t(3)=10, so a(4)=3.
%o A318556 (PARI) t(n) = n*(n+1)*(n+2)/6;
%o A318556 a(n) = my(tn=n*(n+1)*(n+2)/6); sum(k=1, n-1, (tn % t(k)) == 0); \\ _Michel Marcus_, Sep 27 2018
%Y A318556 Cf. A000292.
%K A318556 nonn
%O A318556 1,4
%A A318556 _Torlach Rush_, Aug 28 2018