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 A316856 #7 Jul 15 2018 13:26:19
%S A316856 1,2,4,8,9,16,18,32,36,64,72,81,125,128,144,147,162,195,250,256,288,
%T A316856 294,324,390,500,512,576,588,648,729,780,1000,1024,1125,1152,1176,
%U A316856 1296,1323,1458,1560,1755,2000,2048,2250,2304,2352,2401,2592,2646,2916,3120
%N A316856 Heinz numbers of integer partitions whose reciprocal sum is an integer.
%C A316856 The reciprocal sum of (y_1, ..., y_k) is 1/y_1 + ... + 1/y_k.
%C A316856 The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
%e A316856 195 is the Heinz number of (6,3,2), which has reciprocal sum 1/6 + 1/3 + 1/2 = 1, which is an integer, so 195 belongs to the sequence.
%e A316856 The sequence of all integer partitions whose reciprocal sum is an integer begins: (), (1), (11), (111), (22), (1111), (221), (11111), (2211), (111111), (22111), (2222).
%t A316856 Select[Range[1000],IntegerQ[Sum[m[[2]]/PrimePi[m[[1]]],{m,If[#==1,{},FactorInteger[#]]}]]&]
%Y A316856 Cf. A000041, A051908, A056239, A058360, A072411, A296150, A316854, A316855, A316857.
%K A316856 nonn
%O A316856 1,2
%A A316856 _Gus Wiseman_, Jul 14 2018