cp's OEIS Frontend

A069834 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).

%I A069834 #39 Sep 15 2022 02:22:51
%S A069834 1,3,3,5,15,21,7,9,45,55,33,39,91,105,15,17,153,171,95,105,231,253,69,
%T A069834 75,325,351,189,203,435,465,31,33,561,595,315,333,703,741,195,205,861,
%U A069834 903,473,495,1035,1081,141,147,1225,1275,663,689,1431,1485,385,399
%N A069834 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).
%C A069834 The largest odd divisor of n-th triangular number.
%H A069834 T. D. Noe, <a href="/A069834/b069834.txt">Table of n, a(n) for n = 1..10000</a>
%F A069834 GCD(a(n),a(n+1)) = A000265(n+1). - _Ralf Stephan_, Apr 05 2003
%F A069834 a(n) = A000265(n) * A000265(n+1). - _Franklin T. Adams-Watters_, Nov 20 2009
%F A069834 From _Amiram Eldar_, Sep 15 2022: (Start)
%F A069834 a(n) = A000265(A000217(n)).
%F A069834 Sum_{n>=1} 1/a(n) = Sum_{i,j>=1} 2^(i+1)/(4^i*(2*j-1)^2 - 1) = 2.84288562849221553965... . (End)
%t A069834 Table[tri = n*(n + 1)/2; tri/2^IntegerExponent[tri, 2], {n, 100}] (* _T. D. Noe_, Oct 28 2013 *)
%o A069834 (PARI) for(n=1,100,t=n*n+n;while(t%2==0,t=t/2);print1(t","))
%o A069834 (PARI) a(n)=local(t);t=n*(n+1)\2;t/2^valuation(t,2) \\ _Franklin T. Adams-Watters_, Nov 20 2009
%o A069834 (Python)
%o A069834 def A069834(n):
%o A069834     a, b = divmod(n*n+n, 2)
%o A069834     while b == 0:
%o A069834         a, b = divmod(a,2)
%o A069834     return 2*a+b # _Chai Wah Wu_, Dec 05 2021
%Y A069834 Cf. A000217, A000265, A050605.
%K A069834 nonn
%O A069834 1,2
%A A069834 _Amarnath Murthy_, Apr 14 2002
%E A069834 More terms from _Ralf Stephan_, Apr 05 2003