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 A316899 #8 Aug 27 2018 16:23:06
%S A316899 1,1,1,1,2,2,2,2,3,4,6,6,8,8,10,10,14,14,19,20,25,29,33,34,41,47,54,
%T A316899 61,75,81,97,103,121,132,155,164,200,221,252,274,320,348,405,442,501,
%U A316899 554,639,688,784,854,968,1053,1198,1298,1475,1602,1797,1965,2213,2399
%N A316899 Number of integer partitions of n into relatively prime parts whose reciprocal sum is an integer.
%C A316899 The reciprocal sum of (y_1, ..., y_k) is 1/y_1 + ... + 1/y_k.
%H A316899 Gus Wiseman, <a href="/A051908/a051908.txt">Sequences counting and ranking integer partitions by their reciprocal sums</a>
%e A316899 The a(13) = 8 partitions are (63211), (442111), (33322), (3331111), (2222221), (222211111), (22111111111), (1111111111111).
%t A316899 Table[Length[Select[IntegerPartitions[n],And[GCD@@#==1,IntegerQ[Sum[1/m,{m,#}]]]&]],{n,30}]
%o A316899 (PARI) a(n)={my(s=0); forpart(p=n, if(gcd(p)==1 && frac(sum(i=1, #p, 1/p[i]))==0, s++)); s} \\ _Andrew Howroyd_, Aug 26 2018
%Y A316899 Cf. A000837, A002966, A051908, A058360, A100953, A316854, A316888-A316904.
%K A316899 nonn
%O A316899 1,5
%A A316899 _Gus Wiseman_, Jul 16 2018
%E A316899 a(51)-a(60) from _Andrew Howroyd_, Aug 26 2018