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

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, 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, 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

Offset: 1

Author

Torlach Rush, Aug 28 2018

Keywords

• nonn

Examples

			t(4) is 20 and 20 is divisible by t(1)=1, t(2)=4 and t(3)=10, so a(4)=3.
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000292.

Programs

PARI

t(n) = n*(n+1)*(n+2)/6;
a(n) = my(tn=n*(n+1)*(n+2)/6); sum(k=1, n-1, (tn % t(k)) == 0); \\ Michel Marcus, Sep 27 2018

Formula

a(n) = Sum_{m=1..n-1} [0 = A000292(n) mod A000292(m)]. Here [] is the Iverson bracket function.