cp's OEIS Frontend

A135013 Partial sums of A000265.

%I A135013 #46 Apr 07 2020 14:29:25
%S A135013 1,2,5,6,11,14,21,22,31,36,47,50,63,70,85,86,103,112,131,136,157,168,
%T A135013 191,194,219,232,259,266,295,310,341,342,375,392,427,436,473,492,531,
%U A135013 536,577,598,641,652,697,720,767,770,819,844,895,908,961,988,1043,1050,1107,1136
%N A135013 Partial sums of A000265.
%C A135013 a(n) is also the number of elements in the set {(x,y): 1<=x,y<=n, the fraction x/y reduces to a fraction of the form (odd#)/(odd#)}. - Adam McDougall (mcdougall.adam(AT)gmail.com), Feb 20 2009
%H A135013 G. C. Greubel, <a href="/A135013/b135013.txt">Table of n, a(n) for n = 1..1000</a>
%H A135013 A. Erickson and F. Ruskey, <a href="http://arxiv.org/abs/1304.0070">Enumerating maximal tatami mat coverings of square grids with v vertical dominoes</a>, arXiv:1304.0070 [math.CO], 2013.
%H A135013 R. A. MacLeod, <a href="http://www.jstor.org/stable/2313793">On the Largest Odd Divisor of n</a>, The American Mathematical Monthly, Vol. 75, No. 6 (Jun. - Jul., 1968), pp. 647-648.
%F A135013 a(n) = Sum_{k>=1} (round(n/2^k))^2. - _Alejandro Erickson_, Apr 13 2012
%F A135013 a(n) = n^2/3 + O(n) (see MacLeod link). - _Michel Marcus_, Dec 05 2013
%F A135013 a(j*2^k) = a(j) + (4^k-1)*j^2/3 for any j >= 1, k >= 0. - _Jinyuan Wang_, Mar 23 2019
%t A135013 Accumulate[Table[Times@@(#[[1]]^#[[2]]&/@Select[FactorInteger[i],#[[1]] != 2&]),{i,90}]] (* _Harvey P. Dale_, Jun 25 2013 *)
%o A135013 (HP 50G Calculator) IDIV2 returns quotient & remainder to stack.
%o A135013 << 0 SWAP
%o A135013 WHILE DUP 0 >
%o A135013 REPEAT 2 IDIV2 OVER + SQ ROT + SWAP
%o A135013 END DROP >>
%o A135013 # _Gerald Hillier_, May 02 2009, May 18 2009, Aug 01 2009
%o A135013 (PARI) a(n)=sum(k=1,log(n)\log(2)+1,round(n/2^k)^2) \\ _Charles R Greathouse IV_, Oct 06 2013
%Y A135013 Cf. A000918, A000265, A135014.
%K A135013 nonn
%O A135013 1,2
%A A135013 _N. J. A. Sloane_, Feb 10 2008