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%I #10 Mar 23 2021 15:49:28
%S 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,
%T 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,
%U 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
%N Smallest m such that n divides the tetrahedral number A000292(m+1).
%e 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.
%o (PARI) te(n)=(n+1)*(n+2)*(n+3)/6 for (n=1,50,c=1; while (te(c)%n!=0,c++); print1(c","))
%o (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
%Y Cf. A011772 (triangular numbers), A019554 (squares).
%K nonn
%O 1,3
%A _Jon Perry_, Jul 22 2003
%E More terms from _David Wasserman_, Feb 10 2005
%E Definition corrected by _David A. Corneth_, Mar 22 2021
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