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%I #6 Jun 03 2023 23:56:48
%S 10,21,28,42,55,70,88,91,98,99,132,165,187,198,208,220,231,247,308,
%T 312,325,330,351,363,391,455,462,468,484,520,544,550,551,585,702,713,
%U 715,726,728,770,780,816,819,833,845,975,1073,1078,1092,1144,1170,1210,1216
%N Numbers whose multiset of prime indices satisfies (maximum) - (minimum) = (length).
%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 A061395(a(n)) - A055396(a(n)) = A001222(a(n)).
%e The terms together with their prime indices begin:
%e 10: {1,3}
%e 21: {2,4}
%e 28: {1,1,4}
%e 42: {1,2,4}
%e 55: {3,5}
%e 70: {1,3,4}
%e 88: {1,1,1,5}
%e 91: {4,6}
%e 98: {1,4,4}
%e 99: {2,2,5}
%e 132: {1,1,2,5}
%e 165: {2,3,5}
%e 187: {5,7}
%e 198: {1,2,2,5}
%t prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t Select[Range[100],Max@@prix[#]-Min@@prix[#]==Length[prix[#]]&]
%Y The RHS is A001222.
%Y Partitions of this type are counted by A237832.
%Y The LHS (maximum minus minimum) is A243055.
%Y A001221 (omega) counts distinct prime factors.
%Y A112798 lists prime indices, sum A056239.
%Y A360005 gives median of prime indices, distinct A360457.
%Y Cf. A067801, A111907, A118096, A237821, A361205, A361908, A361909.
%K nonn
%O 1,1
%A _Gus Wiseman_, May 29 2023