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A068443
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Triangular numbers which are the product of two primes.
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13
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6, 10, 15, 21, 55, 91, 253, 703, 1081, 1711, 1891, 2701, 3403, 5671, 12403, 13861, 15931, 18721, 25651, 34453, 38503, 49141, 60031, 64261, 73153, 79003, 88831, 104653, 108811, 114481, 126253, 146611, 158203, 171991, 188191, 218791, 226801
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| These triangular numbers are equal to p * (2p +/- 1).
All a(n) belong to A006987(n) = {6, 10, 15, 20, 21, 28, 35, 36, 45, 55, 56, 66, 70, 78, 84, 91, ...} Binomial coefficients: C(n,k), 2 <= k <= n-2. For n>2 all a(n) are odd and belong to A095147(n) = {15, 21, 35, 45, 55, 91, 105, 153, 165, 171, 231, 253, ...} Odd binomial coefficients: C(n,k), 2 <= k <= n-2. - Alexander Adamchuk, Oct 31 2006
A156592 is a subsequence. [From Reinhard Zumkeller, Feb 10 2009]
A010054(a(n))*A064911(a(n)) = 1. [From Reinhard Zumkeller, Dec 03 2009]
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..1000
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EXAMPLE
| 0,1,3,6,10,... 6=2*3; 2 and 3 are two distinct primes, 10=2*5; 2 and 5 are two distinct primes, ... - Vladimir Orlovsky, Feb 27 2009
a(11) = 1891 and 1891 = 31 * 61
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MATHEMATICA
| Select[ Table[ n(n + 1)/2, {n, 700}], Apply[Plus, Transpose[ FactorInteger[ # ]] [[2]]] == 2 &].
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CROSSREFS
| Cf. A000217, A005382 & A005384.
Cf. A006987, A095147.
Cf. A001358, A005385, A006881, A007304, A066179, A111206, A157342, A157344, A157345, A157346, A157347, A157352, A157353, A157354, A157355, A157356, A157357. - Vladimir Orlovsky, Feb 27 2009
Cf. A164977
Sequence in context: A115744 A122783 A124000 * A113940 A099981 A022949
Adjacent sequences: A068440 A068441 A068442 * A068444 A068445 A068446
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KEYWORD
| easy,nonn
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AUTHOR
| Stephan Wagler (stephanwagler(AT)aol.com), Mar 09 2002
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EXTENSIONS
| Edited by Robert G. Wilson v (rgwv(AT)rgwv.com), Jul 08 2002
Definition corrected by Zak Seidov, Mar 09 2008
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