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
Keywords
Examples
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.
Programs
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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