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 A184199 #18 Jan 11 2021 10:07:48 %S A184199 0,0,1,1,0,1,1,2,1,2,2,4,3,5,4,7,6,10,8,13,11,17,15,23,20,29,26,38,34, %T A184199 49,43,62,55,78,69,97,88,122,109,150,135,186,167,227,205,277,251,337, %U A184199 306,407,371,492,448,591,539,707,647,845,773,1005,922,1193,1096,1412,1298,1667,1535,1963,1809,2305,2127 %N A184199 Number of partitions of n into an odd number of primes. %H A184199 Vaclav Kotesovec, <a href="/A184199/b184199.txt">Table of n, a(n) for n = 0..10000</a> (terms 0..200 from Jean-François Alcover) %F A184199 a(n) = (A000607(n)-A048165(n))/2. %e A184199 n=18 can be partitioned in A000607(18)=19 ways into primes, of which a(18)=8 are odd, namely 11+5+2, 13+3+2, 5+5+3+3+2, 7+3+3+3+2, 7+5+2+2+2, 3+3+3+3+2+2+2, 5+3+2+2+2+2+2, 2+2+2+2+2+2+2+2+2. %e A184199 The remaining A184198(18)=11 are even. %t A184199 a[n_] := a[n] = Count[IntegerPartitions[n, All, Prime[Range[PrimePi[n]]]], p_ /; OddQ[Length[p]]]; %t A184199 Reap[Do[Print[n, " ", a[n]]; Sow[a[n]], {n, 0, 200}]][[2, 1]] (* _Jean-François Alcover_, Feb 13 2020 *) %o A184199 (PARI) %o A184199 parts(n, pred, y)={prod(k=1, n, if(pred(k), 1/(1-y*x^k) + O(x*x^n), 1))} %o A184199 {my(n=80); (Vec(parts(n, isprime, 1)) - Vec(parts(n, isprime, -1)))/2} \\ _Andrew Howroyd_, Dec 28 2017 %Y A184199 Cf. A000607, A048165, A184198, A184172. %K A184199 nonn,easy %O A184199 0,8 %A A184199 _R. J. Mathar_, Jan 10 2011 %E A184199 a(31)-a(70) corrected by _Andrew Howroyd_, Dec 28 2017