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A101745
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Indices of triangular numbers which are 10-almost primes. Indices of A101744.
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1
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255, 384, 511, 575, 639, 728, 767, 896, 1088, 1295, 1376, 1407, 1599, 1700, 1727, 1792, 1919, 1920, 2015, 2024, 2375, 2431, 2672, 2815, 2880, 2915, 2944, 2975, 3104, 3159, 3199, 3327, 3375, 3392, 3456, 3583, 3744, 3999, 4031, 4032, 4160, 4223, 4256
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Mathematica code and extension from Ray Chandler (rayjchandler(AT)sbcglobal.net). These include: T(2^8 - 1) = 32640 = 2^7 * 3 * 5 * 17, T(2^9 - 1) = 130816 = 2^8 * 7 * 73, etc.
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FORMULA
| a(n)*(a(n)+1)/2 has exactly 10 prime factors.
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EXAMPLE
| a(1) = 255 because that is the smallest index of a triangular number which is also a 10-almost prime; specifically T(255) = 255*(255+1)/2 = 32640 = 2^7 * 3 * 5 * 17.
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MATHEMATICA
| BigOmega[n_Integer]:=Plus@@Last[Transpose[FactorInteger[n]]]; Do[ t=n*(n+1)/2; If[BigOmega[t]?10, Print[n, " ", t]; ]; , {n, 2, 5000}];
Flatten[Position[Accumulate[Range[5000]], _?(PrimeOmega[#]==10&)]] (* From Harvey P. Dale, May 12 2011 *)
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CROSSREFS
| Cf. A101744, A000217, A046314, A076550.
Sequence in context: A028526 A132828 A023690 * A053339 A031197 A043348
Adjacent sequences: A101742 A101743 A101744 * A101746 A101747 A101748
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KEYWORD
| easy,nonn
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), Dec 14 2004
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