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 A316891 #8 Jul 18 2018 19:20:37
%S A316891 1,0,0,0,1,0,1,0,2,1,5,2,7,4,7,6,13,7,18,12,20,17,32,20,39,31,47,45,
%T A316891 74,56,96,83,109,105,151,130,199,183,234,232,319,286,404,386,473,488,
%U A316891 638,599,782,767,931,960,1197,1165,1465,1477,1747,1814,2212,2196
%N A316891 Number of aperiodic integer partitions of n into relatively prime parts whose reciprocal sum is an integer.
%C A316891 The reciprocal sum of (y_1, ..., y_k) is 1/y_1 + ... + 1/y_k.
%C A316891 A partition is aperiodic if its multiplicities are relatively prime.
%H A316891 Gus Wiseman, <a href="/A051908/a051908.txt">Sequences counting and ranking integer partitions by their reciprocal sums</a>
%e A316891 The a(17) = 13 partitions:
%e A316891 (6443),
%e A316891 (44441),
%e A316891 (3332222), (6322211),
%e A316891 (44222111),
%e A316891 (222222221), (333221111), (632111111),
%e A316891 (4421111111),
%e A316891 (22222211111), (33311111111),
%e A316891 (2222111111111),
%e A316891 (221111111111111).
%t A316891 Table[Length[Select[IntegerPartitions[n],And[GCD@@#==1,GCD@@Length/@Split[#]==1,IntegerQ[Sum[1/m,{m,#}]]]&]],{n,50}]
%Y A316891 Cf. A000837, A002966, A051908, A058360, A100953, A316854, A316856, A316888-A316904.
%K A316891 nonn
%O A316891 1,9
%A A316891 _Gus Wiseman_, Jul 16 2018
%E A316891 a(51)-a(60) from _Alois P. Heinz_, Jul 18 2018