A085766 Smallest m such that n divides the tetrahedral number A000292(m+1).

1, 1, 6, 1, 2, 6, 4, 5, 24, 2, 8, 6, 10, 5, 7, 13, 14, 25, 16, 3, 6, 9, 20, 7, 22, 10, 78, 5, 26, 7, 28, 29, 8, 14, 4, 25, 34, 17, 24, 7, 38, 6, 40, 9, 24, 21, 44, 15, 46, 22, 15, 11, 50, 78, 8, 5, 16, 26, 56, 7, 58, 29, 25, 61, 12, 42, 64, 14, 43, 13, 68, 53, 70, 34, 24, 17, 19, 25, 76, 13

Offset

1,3

Links

Table of n, a(n) for n=1..80.

Example

Let te(m)=(m+1)(m+2)(m+3)/6. Then te(1)=4, te(2)=10, te(3)=20, te(4)=35, te(5)=56 and te(6)=84. te(6) is the first tetrahedral number divisible by 3, hence a(3)=6.

Prog

(PARI) te(n)=(n+1)*(n+2)*(n+3)/6 for (n=1, 50, c=1; while (te(c)%n!=0, c++); print1(c", "))
(PARI) first(n) = {my(res = vector(n), todo = n); res[1] = 1; todo--; for(i = 1, oo, t = binomial(i + 2, 3); d = divisors(t); for(j = 1, #d, if(d[j] <= n && res[d[j]] == 0, res[d[j]] = i - 1; todo--; if(todo <= 0, return(res); ) ) ) ) } \\ David A. Corneth, Mar 22 2021

Crossrefs

Cf. A011772 (triangular numbers), A019554 (squares).

Sequence in context: A070682 A216415 A112828 * A002329 A053453 A347197

Adjacent sequences: A085763 A085764 A085765 * A085767 A085768 A085769

Keyword

nonn

Author

Jon Perry, Jul 22 2003

Extensions

More terms from David Wasserman, Feb 10 2005

Definition corrected by David A. Corneth, Mar 22 2021

Status

approved