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 A292587 #26 Sep 26 2017 20:28:21 %S A292587 0,1,1,2,1,3,1,4,2,3,1,5,1,3,3,7,1,5,1,5,3,3,1,8,2,3,4,5,1,6,1,11,3,3, %T A292587 3,23,1,3,3,8,1,6,1,5,5,3,1,12,2,5,3,5,1,8,3,8,3,3,1,9,1,3,5,22,3,6,1, %U A292587 5,3,6,1,38,1,3,5,5,3,6,1,12,7,3,1,9,3,3,3,8,1,9,3,5,3,3,3,17,1,5,5,23,1,6,1,8,6 %N A292587 Compound filter: a(n) = P(A001221(n), A292582(n)), where P(n,k) is sequence A000027 used as a pairing function. %C A292587 This is essentially also a filter constructed from the runlengths of numbers of the form 4k+0 and the runlengths of numbers of the form 4k+2 encountered in trajectories of A005940-tree. See comments in A083399 and A292586. %C A292587 For all i, j: A291757(i) = A291757(j) => a(i) = a(j), that is, this filter matches to a subset of the sequences matched by filter A291757. %C A292587 Moreover, for all i, j: a(i) = a(j) <=> A101296(i) = A101296(j), thus the subset is exactly the sequences matched by A101296 (A046523). This follows because the prime signature of n can be recovered from the two components as A046523(n) = A046523(A003557(n)) * A292586(n) and also vice versa as A046523(A003557(n)) = A003557(A046523(n)). %H A292587 Antti Karttunen, <a href="/A292587/b292587.txt">Table of n, a(n) for n = 1..16384</a> %H A292587 <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a> %F A292587 a(n) = (1/2)*(2 + ((A001221(n) + A292582(n))^2) - A001221(n) - 3*A292582(n)). %Y A292587 Cf. A000027, A001221, A003557, A005940, A046523, A101296, A291757, A292582, A292584, A292586, A292588. %K A292587 nonn,less %O A292587 1,4 %A A292587 _Antti Karttunen_, Sep 26 2017