A342808 Smallest k such that the k-th tetrahedral number is divisible by exactly n tetrahedral numbers.

1, 2, 6, 4, 8, 28, 14, 48, 55, 98, 154, 54, 495, 1034, 504, 559, 208, 440, 2078, 2000, 350, 3519, 6578, 2574, 5983, 2924, 21734, 25023, 11934, 30303, 120175, 81718, 11438, 73150, 71630, 43470, 50048, 511784, 371448, 37960, 1478048, 391950, 812174, 393470, 217854, 576288

Offset

1,2

Links

Table of n, a(n) for n=1..46.

Example

a(6) = 28 as the 28th tetrahedral number, binomial(28+2, 3) = 4060, is divisible by 6 tetrahedral numbers namely 1, 4, 10, 20, 35 and 4060.

Prog

(PARI) first(n) = { my(res = vector(n), todo = n); for(i = 1, oo, c = f(i); if(c <= n && res[c] == 0, res[c] = i; todo--; if(todo <= 0, return(res)))) }
f(n) = my(d = divisors(binomial(n + 2, 3))); #select(x -> istetra(x), d) istetra(n)= my(k = sqrtnint(6*n, 3)); binomial(k + 2, 3) == n

Crossrefs

Cf. A000292, A076983, A318556, A319788.

Sequence in context: A352768 A352867 A324651 * A201895 A192408 A074208

Adjacent sequences: A342805 A342806 A342807 * A342809 A342810 A342811

Keyword

nonn

Author

David A. Corneth, Mar 22 2021

Status

approved