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A069834
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a(n) = n-th reduced triangular number: n*(n+1)/{2^k} where 2^k is the largest power of 2 that divides product n*(n+1).
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10
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1, 3, 3, 5, 15, 21, 7, 9, 45, 55, 33, 39, 91, 105, 15, 17, 153, 171, 95, 105, 231, 253, 69, 75, 325, 351, 189, 203, 435, 465, 31, 33, 561, 595, 315, 333, 703, 741, 195, 205, 861, 903, 473, 495, 1035, 1081, 141, 147, 1225, 1275, 663, 689, 1431, 1485, 385, 399
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OFFSET
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1,2
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COMMENTS
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The largest odd divisor of n-th triangular number.
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LINKS
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FORMULA
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Sum_{n>=1} 1/a(n) = Sum_{i,j>=1} 2^(i+1)/(4^i*(2*j-1)^2 - 1) = 2.84288562849221553965... . (End)
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MATHEMATICA
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Table[tri = n*(n + 1)/2; tri/2^IntegerExponent[tri, 2], {n, 100}] (* T. D. Noe, Oct 28 2013 *)
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PROG
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(PARI) for(n=1, 100, t=n*n+n; while(t%2==0, t=t/2); print1(t", "))
(Python)
a, b = divmod(n*n+n, 2)
while b == 0:
a, b = divmod(a, 2)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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