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A128905
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Numbers n such that n-th triangular number has exactly four distinct prime factors.
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0
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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; internal format)
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OFFSET
| 1,1
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COMMENTS
| Or, indices of triangular numbers with exactly four distinct prime factors.
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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 triangular number and p, q, r, s are distinct primes.
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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.
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CROSSREFS
| Cf. A000217, A068443, A069903, A076551, A127637, A128896.
Sequence in context: A115882 A007589 A049390 * A183047 A205220 A188250
Adjacent sequences: A128902 A128903 A128904 * A128906 A128907 A128908
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KEYWORD
| nonn
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AUTHOR
| Zak Seidov (zakseidov(AT)gmail.com), Apr 22 2007
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