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%I #24 Mar 23 2021 15:52:46
%S 1,2,6,4,8,28,14,48,55,98,154,54,495,1034,504,559,208,440,2078,2000,
%T 350,3519,6578,2574,5983,2924,21734,25023,11934,30303,120175,81718,
%U 11438,73150,71630,43470,50048,511784,371448,37960,1478048,391950,812174,393470,217854,576288
%N Smallest k such that the k-th tetrahedral number is divisible by exactly n tetrahedral numbers.
%e 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.
%o (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)))) }
%o 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
%Y Cf. A000292, A076983, A318556, A319788.
%K nonn
%O 1,2
%A _David A. Corneth_, Mar 22 2021
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