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 A071640 #22 Jun 11 2019 05:36:49 %S A071640 1,1,2,3,4,5,6,6,6,6,6,7,8,9,9,10,11,12,12,13,13,13,14,15,15,15,15,15, %T A071640 16,16,16,17,18,18,19,20,21,22,23,23,24,24,25,26,26,26,26,27,28,28,29, %U A071640 30,31,32,32,33,33,33,33,34,35,35,36,36,36,36,37,38,39,39,40,41,42,42 %N A071640 a(n) = Sum_{i=1..n} A040051(i). %C A071640 Does 2*a(n) > n for n>2? Cf. A086144. - _Benoit Cloitre_ %C A071640 No. First failure is at n = 6662. - _Peter Luschny_, Oct 05 2011 %H A071640 T. D. Noe, <a href="/A071640/b071640.txt">Table of n, a(n) for n = 1..1000</a> %p A071640 A071640 := proc(n) option remember; if n=1 then 1 else A071640(n-1)+ %p A071640 (combinat[numbpart](n) mod 2) fi end: # _Peter Luschny_, Oct 05 2011 %t A071640 a[n_] := Sum[Mod[PartitionsP[i], 2], {i, 1, n}]; %t A071640 Array[a, 80] (* _Jean-François Alcover_, Jun 03 2019 *) %o A071640 (PARI) a(n) = my(x='x+O('x^(n+1)), p = 1/eta(x)); sum(i=1, n, (1-(-1)^(polcoeff(p, i))))/2; \\ corrected by _Michel Marcus_, Jun 11 2019 %Y A071640 Cf. A000041, A086144, A040051, A087177. %K A071640 easy,nonn %O A071640 1,3 %A A071640 _Benoit Cloitre_, Jun 22 2002