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 A347286 #57 Oct 14 2021 18:11:13 %S A347286 0,1,1,3,3,4,5,7,6,8,9,10,11,12,11,15,15,15,17,18,17,20,21,22,22,24, %T A347286 23,26,27,26,29,31,29,32,31,33,35,36,35,38,39,38,41,42,39,44,45,46,46, %U A347286 47,47,50,51,50,51,54,53,56,57,56,59,60,57,63,61,62,65,66,65,66 %N A347286 a(n) is n minus the number of odd divisors of n. %C A347286 a(n) is n minus the number of partitions of n into consecutive parts. %C A347286 This definition is in accordance with the diagram as shown below in the Example section which also appears in many sequences related to A237048, A237591, A237593 and possible others. %C A347286 a(n) is also the number of zeros in the n-th row of A285898. %F A347286 a(n) = n - A001227(n). %e A347286 For n = 18 the divisors of 18 are 1, 2, 3, 6, 9, 18. There are three odd divisors: 1, 3, 9, so a(18) = 18 - 3 = 15. %e A347286 On the other hand the partitions of 18 into consecutive parts are [18], [7, 6, 5], [6, 5, 4, 3]. There are three of such partitions, so a(18) = 18 - 3 = 15. %e A347286 Illustration of initial terms: %e A347286 . %e A347286 n a(n) Diagram _ %e A347286 1 0 _|x| %e A347286 2 1 _|x _| %e A347286 3 1 _|x |x| %e A347286 4 3 _|x _| | %e A347286 5 3 _|x |x _| %e A347286 6 4 _|x _| |x| %e A347286 7 5 _|x |x | | %e A347286 8 7 _|x _| _| | %e A347286 9 6 _|x |x |x _| %e A347286 10 8 _|x _| | |x| %e A347286 11 9 _|x |x _| | | %e A347286 12 10 _|x _| |x | | %e A347286 13 11 _|x |x | _| | %e A347286 14 12 _|x _| _| |x _| %e A347286 15 11 _|x |x |x | |x| %e A347286 16 15 _|x _| | | | | %e A347286 17 15 _|x |x _| _| | | %e A347286 18 15 _|x _| |x |x | | %e A347286 19 17 _|x |x | | _| | %e A347286 20 18 _|x _| _| | |x _| %e A347286 21 17 |x |x |x | | |x| %e A347286 ... %e A347286 In the above diagram the number of x's in row n equals A001227(n), the number of partitions n into consecutive parts. %e A347286 a(n) is the number of square cells in row n that do not contain a "x". %e A347286 In other words: a(n) is the number of square cells in row n that do not have a horizontal line segment above. %t A347286 a[n_] := n - DivisorSigma[0, n/2^IntegerExponent[n, 2]]; Array[a, 70] (* _Amiram Eldar_, Sep 12 2021 *) %o A347286 (PARI) a(n) = n - sumdiv(n, d, d%2); \\ _Michel Marcus_, Sep 12 2021 %Y A347286 Cf. A001227, A196020, A204217, A235791, A237048, A237591, A237593, A238005, A245092, A285898, A286000, A286001. %K A347286 nonn,easy %O A347286 1,4 %A A347286 _Omar E. Pol_, Sep 12 2021