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A128905
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Numbers k such that the k-th triangular number has exactly four distinct prime factors.
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2
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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
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OFFSET
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1,1
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COMMENTS
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Or, indices of triangular numbers with exactly four distinct prime factors.
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LINKS
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FORMULA
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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.
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EXAMPLE
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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
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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