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%I #8 Sep 30 2022 07:50:43
%S 35,65,70,95,105,130,140,143,145,169,175,185,190,195,209,210,215,245,
%T 247,253,260,265,280,285,286,290,305,315,319,323,325,338,350,355,370,
%U 377,380,385,390,391,395,407,418,420,429,430,435,445,455,473,475,481,490
%N Numbers with (WLOG adjacent) prime indices x <= y such that the greatest prime factor of x is greater than the least prime factor of y.
%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. The multiset of multisets with MM-number n is formed by taking the multiset of prime indices of each part of the multiset of prime indices of n. For example, the prime indices of 78 are {1,2,6}, so the multiset of multisets with MM-number 78 is {{},{1},{1,2}}.
%e The terms and corresponding multisets of multisets:
%e 35: {{2},{1,1}}
%e 65: {{2},{1,2}}
%e 70: {{},{2},{1,1}}
%e 95: {{2},{1,1,1}}
%e 105: {{1},{2},{1,1}}
%e 130: {{},{2},{1,2}}
%e 140: {{},{},{2},{1,1}}
%e 143: {{3},{1,2}}
%e 145: {{2},{1,3}}
%e 169: {{1,2},{1,2}}
%e 175: {{2},{2},{1,1}}
%e 185: {{2},{1,1,2}}
%t primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t Select[Range[100],MatchQ[primeMS[#],{___,x_,y_,___}/;Max@@primeMS[x]>Min@@primeMS[y]]&]
%t Select[Range[100],!LessEqual@@Join@@primeMS/@primeMS[#]&]
%Y These are the positions of non-weakly increasing rows in A357139.
%Y A000961 lists prime powers.
%Y A003963 multiples prime indices.
%Y A056239 adds up prime indices.
%Y Cf. A000720, A001221, A001222, A007716, A275024, A302242, A302243, A302505, A324926, A325032, A325034.
%K nonn
%O 1,1
%A _Gus Wiseman_, Sep 30 2022
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