cp's OEIS Frontend

A363222 Numbers whose multiset of prime indices satisfies (maximum) - (minimum) = (length).

%I A363222 #6 Jun 03 2023 23:56:48
%S A363222 10,21,28,42,55,70,88,91,98,99,132,165,187,198,208,220,231,247,308,
%T A363222 312,325,330,351,363,391,455,462,468,484,520,544,550,551,585,702,713,
%U A363222 715,726,728,770,780,816,819,833,845,975,1073,1078,1092,1144,1170,1210,1216
%N A363222 Numbers whose multiset of prime indices satisfies (maximum) - (minimum) = (length).
%C A363222 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 A363222 A061395(a(n)) - A055396(a(n)) = A001222(a(n)).
%e A363222 The terms together with their prime indices begin:
%e A363222     10: {1,3}
%e A363222     21: {2,4}
%e A363222     28: {1,1,4}
%e A363222     42: {1,2,4}
%e A363222     55: {3,5}
%e A363222     70: {1,3,4}
%e A363222     88: {1,1,1,5}
%e A363222     91: {4,6}
%e A363222     98: {1,4,4}
%e A363222     99: {2,2,5}
%e A363222    132: {1,1,2,5}
%e A363222    165: {2,3,5}
%e A363222    187: {5,7}
%e A363222    198: {1,2,2,5}
%t A363222 prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A363222 Select[Range[100],Max@@prix[#]-Min@@prix[#]==Length[prix[#]]&]
%Y A363222 The RHS is A001222.
%Y A363222 Partitions of this type are counted by A237832.
%Y A363222 The LHS (maximum minus minimum) is A243055.
%Y A363222 A001221 (omega) counts distinct prime factors.
%Y A363222 A112798 lists prime indices, sum A056239.
%Y A363222 A360005 gives median of prime indices, distinct A360457.
%Y A363222 Cf. A067801, A111907, A118096, A237821, A361205, A361908, A361909.
%K A363222 nonn
%O A363222 1,1
%A A363222 _Gus Wiseman_, May 29 2023