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%I #8 Jul 14 2021 01:59:57
%S 20,51,59,60,65,68,69,76,77,83,91,92,105,110,114,115,123,129,131,139,
%T 154,156,165,182,185,186,187,194,210,212,221,227,228,235,236,237,246,
%U 254,258,265,266,267,273,276,286,290,291,307,309,318,321,322,330,345
%N Numbers k such that the k-th triangular number has exactly four distinct prime factors.
%C Or, indices of triangular numbers with exactly four distinct prime factors.
%F a(n)=k and T(k)=k(k+1)/2=p*q*r*s for some k, p, q, r, s where T(k) is a triangular number and p, q, r, s are distinct primes.
%e In order of increasing p (the least prime factor of T(k)):
%e a(1) = 20 because T(20) = 210 = 2* 3* 5* 7,
%e a(5) = 65 because T(65) = 2145 = 3* 5*11*13,
%e a(21) = 154 because T(154) = 11935 = 5* 7*11*31,
%e a(45) = 286 because T(286) = 41041 = 7*11*13*41,
%e a(143)= 781 because T(781) = 305371 = 11*17*23*71,
%e a(91) = 493 because T(493) = 121771 = 13*17*19*29, etc.
%Y Cf. A000217, A068443, A069903, A076551, A127637, A128896.
%K nonn
%O 1,1
%A _Zak Seidov_, Apr 22 2007
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