This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A284475 #36 May 20 2017 22:17:55 %S A284475 0,2,1,6,3,8,5,14,7,13,9,24,11,19,13,30,15,31,17,36,20,31,21,56,23,37, %T A284475 28,48,27,59,29,62,36,49,33,79,35,55,44,84,39,81,41,75,52,67,45,120, %U A284475 47,83,60,89,51,103,54,112,68,85,57,151,59,91,76,126,66,125,65,117,84,127,69,182,71,109,97,131,75,148 %N A284475 Total number of parts in all partitions of n into equal parts, minus the total number of parts in all partitions of n into consecutive parts. %C A284475 Observation: at least for the first 78 terms of this sequence the values of n where a(n) = n - 2 coincide with the odd numbers of A082664. %F A284475 Conjecture: a(n) = A000203(n) - A204217(n). %F A284475 a(2^k) = A000918(k+1), k>=0. %e A284475 For n = 10 the partitions of 10 into equal parts are [10], [5, 5], [2, 2, 2, 2, 2] and [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]. The total number of parts is 18. On the other hand, the partitions of 10 into consecutive parts are [10] and [4, 3, 2, 1]. The total number of parts is 5, so a(10) = 18 - 5 = 13. %Y A284475 Cf. A000203, A000918, A082647, A082664, A204217, A285914. %K A284475 nonn %O A284475 1,2 %A A284475 _Omar E. Pol_, May 03 2017