cp's OEIS Frontend

A363134 Positive integers whose multiset of prime indices satisfies: (length) = 2*(minimum).

%I A363134 #5 Jun 05 2023 17:07:20
%S A363134 4,6,10,14,22,26,34,38,46,58,62,74,81,82,86,94,106,118,122,134,135,
%T A363134 142,146,158,166,178,189,194,202,206,214,218,225,226,254,262,274,278,
%U A363134 297,298,302,314,315,326,334,346,351,358,362,375,382,386,394,398,422,441
%N A363134 Positive integers whose multiset of prime indices satisfies: (length) = 2*(minimum).
%C A363134 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 A363134 A001222(a(n)) = 2*A055396(a(n)).
%e A363134 The terms together with their prime indices begin:
%e A363134      4: {1,1}         94: {1,15}       214: {1,28}
%e A363134      6: {1,2}        106: {1,16}       218: {1,29}
%e A363134     10: {1,3}        118: {1,17}       225: {2,2,3,3}
%e A363134     14: {1,4}        122: {1,18}       226: {1,30}
%e A363134     22: {1,5}        134: {1,19}       254: {1,31}
%e A363134     26: {1,6}        135: {2,2,2,3}    262: {1,32}
%e A363134     34: {1,7}        142: {1,20}       274: {1,33}
%e A363134     38: {1,8}        146: {1,21}       278: {1,34}
%e A363134     46: {1,9}        158: {1,22}       297: {2,2,2,5}
%e A363134     58: {1,10}       166: {1,23}       298: {1,35}
%e A363134     62: {1,11}       178: {1,24}       302: {1,36}
%e A363134     74: {1,12}       189: {2,2,2,4}    314: {1,37}
%e A363134     81: {2,2,2,2}    194: {1,25}       315: {2,2,3,4}
%e A363134     82: {1,13}       202: {1,26}       326: {1,38}
%e A363134     86: {1,14}       206: {1,27}       334: {1,39}
%t A363134 prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A363134 Select[Range[100],Length[prix[#]]==2*Min[prix[#]]&]
%Y A363134 Partitions of this type are counted by A237757.
%Y A363134 Removing the factor 2 gives A324522.
%Y A363134 For maximum instead of length we have A361908, counted by A118096.
%Y A363134 For mean instead of length we have A363133, counted by A363132.
%Y A363134 For maximum instead of minimum we have A363218, counted by A237753.
%Y A363134 A055396 gives minimum prime index, maximum A061395.
%Y A363134 A112798 lists prime indices, length A001222, sum A056239.
%Y A363134 A360005 gives twice median of prime indices.
%Y A363134 Cf. A000961, A006141, A046660, A051293, A106529, A111907, A237755, A237824, A327482, A361860, A361861, A362050.
%K A363134 nonn
%O A363134 1,1
%A A363134 _Gus Wiseman_, Jun 05 2023