|
%I #24 Dec 31 2020 11:11:15
%S 0,0,2,2,4,4,6,6,8,10,12,12,14,16,18,18,20,22,24,24,28,30,32,32,34,36,
%T 40,40,42,44,46,46,50,52,54,56,58,60,64,64,66,68,70,72,76,78,80,80,82,
%U 84,88,90,92,94,98,98,102,104,106,108,110,112,116,116,120,122,124,126,130,132,134,134,136,138,144,146,148,152
%N Total number of odd divisors of all positive integers <= n, minus the total number of middle divisors of all positive integers <= n.
%C Conjecture 1: a(n) is also twice the total number of partitions of all positive integers <= n into an even number of consecutive parts.
%C Conjecture 2: a(n) is also the total number of equidistant subparts of the symmetric representations of sigma of all positive integers <= n. Thus a(n) is also the total number of equidistant subparts in the terraces of the stepped pyramid with n levels described in A245092.
%C For more information about the "subparts" of the symmetric representation of sigma see A279387 and A237593.
%F Conjecture: a(n) = A060831(n) - A240542(n).
%F Conjecture: a(n) = 2*A285902(n).
%t Accumulate@ Table[DivisorSum[n, 1 &, OddQ] - DivisorSum[n, 1 &, Sqrt[n/2] <= # < Sqrt[2 n] &], {n, 78}] (* _Michael De Vlieger_, May 18 2017 *)
%Y Partial sums of A281009.
%Y Cf. A060831, A196020, A235791, A236104, A237048, A237591, A237593, A240542, A245092, A279387, A285901, A285902.
%K nonn
%O 1,3
%A _Omar E. Pol_, May 14 2017
|
