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A128905

Numbers k such that the k-th triangular number has exactly four distinct prime factors.

20, 51, 59, 60, 65, 68, 69, 76, 77, 83, 91, 92, 105, 110, 114, 115, 123, 129, 131, 139, 154, 156, 165, 182, 185, 186, 187, 194, 210, 212, 221, 227, 228, 235, 236, 237, 246, 254, 258, 265, 266, 267, 273, 276, 286, 290, 291, 307, 309, 318, 321, 322, 330, 345

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OFFSET

1,1

COMMENTS

Or, indices of triangular numbers with exactly four distinct prime factors.

LINKS

Table of n, a(n) for n=1..54.

FORMULA

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.

EXAMPLE

In order of increasing p (the least prime factor of T(k)):

a(1) = 20 because T(20) = 210 = 2* 3* 5* 7,