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%I #5 Jun 05 2023 17:07:20
%S 4,6,10,14,22,26,34,38,46,58,62,74,81,82,86,94,106,118,122,134,135,
%T 142,146,158,166,178,189,194,202,206,214,218,225,226,254,262,274,278,
%U 297,298,302,314,315,326,334,346,351,358,362,375,382,386,394,398,422,441
%N Positive integers whose multiset of prime indices satisfies: (length) = 2*(minimum).
%C A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
%F A001222(a(n)) = 2*A055396(a(n)).
%e The terms together with their prime indices begin:
%e 4: {1,1} 94: {1,15} 214: {1,28}
%e 6: {1,2} 106: {1,16} 218: {1,29}
%e 10: {1,3} 118: {1,17} 225: {2,2,3,3}
%e 14: {1,4} 122: {1,18} 226: {1,30}
%e 22: {1,5} 134: {1,19} 254: {1,31}
%e 26: {1,6} 135: {2,2,2,3} 262: {1,32}
%e 34: {1,7} 142: {1,20} 274: {1,33}
%e 38: {1,8} 146: {1,21} 278: {1,34}
%e 46: {1,9} 158: {1,22} 297: {2,2,2,5}
%e 58: {1,10} 166: {1,23} 298: {1,35}
%e 62: {1,11} 178: {1,24} 302: {1,36}
%e 74: {1,12} 189: {2,2,2,4} 314: {1,37}
%e 81: {2,2,2,2} 194: {1,25} 315: {2,2,3,4}
%e 82: {1,13} 202: {1,26} 326: {1,38}
%e 86: {1,14} 206: {1,27} 334: {1,39}
%t prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t Select[Range[100],Length[prix[#]]==2*Min[prix[#]]&]
%Y Partitions of this type are counted by A237757.
%Y Removing the factor 2 gives A324522.
%Y For maximum instead of length we have A361908, counted by A118096.
%Y For mean instead of length we have A363133, counted by A363132.
%Y For maximum instead of minimum we have A363218, counted by A237753.
%Y A055396 gives minimum prime index, maximum A061395.
%Y A112798 lists prime indices, length A001222, sum A056239.
%Y A360005 gives twice median of prime indices.
%Y Cf. A000961, A006141, A046660, A051293, A106529, A111907, A237755, A237824, A327482, A361860, A361861, A362050.
%K nonn
%O 1,1
%A _Gus Wiseman_, Jun 05 2023
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