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 A335376 #6 Jun 05 2020 09:57:18
%S A335376 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,
%T A335376 28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,51,
%U A335376 52,53,55,56,57,58,59,61,62,63,64,65,66,67,68,69,70,71
%N A335376 Heinz numbers of totally co-strong integer partitions.
%C A335376 First differs from A242031 and A317257 in lacking 60.
%C A335376 A sequence is totally co-strong if it is empty, equal to (1), or its run-lengths are weakly increasing (co-strong) and are themselves a totally co-strong sequence.
%C A335376 The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k). This gives a bijective correspondence between positive integers and integer partitions.
%e A335376 The sequence of terms together with their prime indices begins:
%e A335376 1: {} 16: {1,1,1,1} 32: {1,1,1,1,1}
%e A335376 2: {1} 17: {7} 33: {2,5}
%e A335376 3: {2} 19: {8} 34: {1,7}
%e A335376 4: {1,1} 20: {1,1,3} 35: {3,4}
%e A335376 5: {3} 21: {2,4} 36: {1,1,2,2}
%e A335376 6: {1,2} 22: {1,5} 37: {12}
%e A335376 7: {4} 23: {9} 38: {1,8}
%e A335376 8: {1,1,1} 24: {1,1,1,2} 39: {2,6}
%e A335376 9: {2,2} 25: {3,3} 40: {1,1,1,3}
%e A335376 10: {1,3} 26: {1,6} 41: {13}
%e A335376 11: {5} 27: {2,2,2} 42: {1,2,4}
%e A335376 12: {1,1,2} 28: {1,1,4} 43: {14}
%e A335376 13: {6} 29: {10} 44: {1,1,5}
%e A335376 14: {1,4} 30: {1,2,3} 45: {2,2,3}
%e A335376 15: {2,3} 31: {11} 46: {1,9}
%e A335376 For example, 180 is the Heinz number of (3,2,2,1,1) which has run-lengths: (1,2,2) -> (1,2) -> (1,1) -> (2) -> (1). All of these are weakly increasing, so 180 is in the sequence.
%t A335376 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A335376 totcostrQ[q_]:=Or[Length[q]<=1,And[OrderedQ[Length/@Split[q]],totcostrQ[Length/@Split[q]]]];
%t A335376 Select[Range[100],totcostrQ[Reverse[primeMS[#]]]&]
%Y A335376 Partitions with weakly increasing run-lengths are A100883.
%Y A335376 Totally strong partitions are counted by A316496.
%Y A335376 The strong version is A316529.
%Y A335376 The version for reversed partitions is (also) A316529.
%Y A335376 These partitions are counted by A332275.
%Y A335376 The widely normal version is A332293.
%Y A335376 The complement is A335377.
%Y A335376 Cf. A100882, A133808, A181819, A182850, A242031, A305732, A317256, A317258, A329747, A332291.
%K A335376 nonn
%O A335376 1,2
%A A335376 _Gus Wiseman_, Jun 04 2020