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A128905 Numbers k such that the k-th triangular number has exactly four distinct prime factors. 2
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 (list; graph; refs; listen; history; text; internal format)
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,

  a(5)  =  65 because T(65)  =   2145 =  3* 5*11*13,

  a(21) = 154 because T(154) =  11935 =  5* 7*11*31,

  a(45) = 286 because T(286) =  41041 =  7*11*13*41,

  a(143)= 781 because T(781) = 305371 = 11*17*23*71,

  a(91) = 493 because T(493) = 121771 = 13*17*19*29, etc.

CROSSREFS

Cf. A000217, A068443, A069903, A076551, A127637, A128896.

Sequence in context: A345124 A049390 A220040 * A276135 A350115 A211143

Adjacent sequences:  A128902 A128903 A128904 * A128906 A128907 A128908

KEYWORD

nonn

AUTHOR

Zak Seidov, Apr 22 2007

STATUS

approved

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Last modified January 28 11:01 EST 2022. Contains 350655 sequences. (Running on oeis4.)