A225400 - OEIS

%I #9 May 07 2013 13:31:15

%S 0,3,8,14,15,39,20,44,35,195,119,104,594,224,384,455,539,440,560,3080,

%T 2184,1539,2015,2639,5264,4199,15399,13299,8855,23919,2079,30744,

%U 43680,36575,14399,5984,58695,113399,47124,107184,12375,78624,98175,73359,111320,242879

%N First occurrence of n in A225399, or -1 if n does not appear in A225399.

%C Index of the least triangular number t divisible by exactly n triangular numbers bigger than 1 and less than t, or -1 if there is no such t.

%C Conjecture: a(n) >= 0.

%F A000217(a(n)) = A076983(n+1) for n>0, if the conjecture is true and a(n) >= 0.

%t mx = 10000; tri = Table[n (n + 1)/2, {n, mx}]; nn = 20; t = Table[0, {nn}]; found = 0; n = 0; While[n < mx && found < nn, n++; cnt = 0; Do[If[Mod[tri[[n]], tri[[k]]] == 0, cnt++], {k, 2, n - 1}]; If[cnt <= nn && t[[cnt]] == 0, t[[cnt]] = n; found++]]; Join[{0}, t] (* _T. D. Noe_, May 07 2013 *)

%o (C)

%o #include <stdio.h>

%o #define TOP 80

%o int main() {

%o   unsigned long long c, i, j, t, tn;

%o   long long f[TOP];

%o   memset(f, -1, sizeof(f));

%o   for (i = tn = 0; i < (1ULL<<32); i++) {

%o         for (c=0, tn += i, t = j = 3; t*2 <= tn; t+=j, ++j)

%o                 if (tn%t==0) ++c;

%o         if (c<TOP && f[c]<0)

%o                 for (printf("\n"), f[c]=i, j=0; j<TOP; ++j)

%o                         printf("%lld, ", f[j]);

%o   }

%o   return 0;

%o }

%Y Cf. A000217, A225399, A076983.

%K nonn

%O 0,2

%A _Alex Ratushnyak_, May 06 2013