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 A316888 #7 Jul 16 2018 21:46:55
%S A316888 2,195,3185,6475,10527,16401,20445,20535,21045,25365,46155,164255,
%T A316888 171941,218855,228085,267883,312785,333925,333935,335405,343735,
%U A316888 355355,414295,442975,474513,527425,549575,607475,633777,691041,711321,722425,753865,804837,822783
%N A316888 Heinz numbers of aperiodic integer partitions into relatively prime parts whose reciprocal sum is 1.
%C A316888 The reciprocal sum of (y_1, ..., y_k) is 1/y_1 + ... + 1/y_k.
%C A316888 The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
%C A316888 A partition is aperiodic if its multiplicities are relatively prime.
%C A316888 Does not contain 29888089, which belongs to A316890 and is the Heinz number of a periodic partition.
%H A316888 Gus Wiseman, <a href="/A051908/a051908.txt">Sequences counting and ranking integer partitions by their reciprocal sums</a>
%e A316888 The partition (6,4,4,3) with Heinz number 3185 is aperiodic, has relatively prime parts, and 1/6 + 1/4 + 1/4 + 1/3 = 1, so 3185 belongs to the sequence.
%e A316888 The sequence of partitions whose Heinz numbers belong to the sequence begins: (1), (6,3,2), (6,4,4,3), (12,4,3,3), (10,5,5,2), (20,5,4,2), (15,10,3,2), (12,12,3,2), (18,9,3,2), (24,8,3,2), (42,7,3,2).
%t A316888 Select[Range[2,100000],And[GCD@@FactorInteger[#][[All,2]]==1,GCD@@PrimePi/@FactorInteger[#][[All,1]]==1,Sum[m[[2]]/PrimePi[m[[1]]],{m,FactorInteger[#]}]==1]&]
%Y A316888 Cf. A000837, A002966, A007916, A051908, A100953, A289509, A296150, A316855, A316856, A316857, A316888-A316904.
%K A316888 nonn
%O A316888 1,1
%A A316888 _Gus Wiseman_, Jul 16 2018