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 A322136 #4 Nov 28 2018 08:03:04
%S A322136 4,8,12,16,24,32,36,40,48,64,72,80,96,108,112,120,128,144,160,192,216,
%T A322136 224,240,256,288,320,324,336,352,360,384,400,432,448,480,512,576,640,
%U A322136 648,672,704,720,768,800,832,864,896,960,972
%N A322136 Numbers whose number of prime factors counted with multiplicity exceeds half their sum of prime indices by at least 1.
%C A322136 The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k). The sequence lists all Heinz numbers of integer partitions where the number of parts is at least 1 plus half the sum of parts.
%C A322136 Also Heinz numbers of integer partitions that are the vertex-degrees of some hypertree. We allow no singletons in a hypertree, so 2 is not included.
%e A322136 The sequence of partitions with Heinz numbers in the sequence begins: (11), (111), (211), (1111), (2111), (11111), (2211), (3111), (21111), (111111), (22111), (31111), (211111), (22211), (41111), (32111), (1111111).
%t A322136 Select[Range[1000],PrimeOmega[#]>=(Total[Cases[FactorInteger[#],{p_,k_}:>k*PrimePi[p]]]+2)/2&]
%Y A322136 Cf. A000569, A025065, A030019, A056156, A056239, A056503, A112798, A181821, A242414, A304382, A320922, A320923, A320924, A320925.
%K A322136 nonn
%O A322136 1,1
%A A322136 _Gus Wiseman_, Nov 27 2018