cp's OEIS Frontend

A360558 Numbers whose multiset of prime factors (or indices, see A112798) has more adjacent equalities (or parts that have appeared before) than distinct parts.

%I A360558 #6 Feb 21 2023 23:24:39
%S A360558 8,16,27,32,48,64,72,80,81,96,108,112,125,128,144,160,162,176,192,200,
%T A360558 208,216,224,243,256,272,288,304,320,324,343,352,368,384,392,400,405,
%U A360558 416,432,448,464,480,486,496,500,512,544,567,576,592,608,625,640,648
%N A360558 Numbers whose multiset of prime factors (or indices, see A112798) has more adjacent equalities (or parts that have appeared before) than distinct parts.
%C A360558 No terms are squarefree.
%C A360558 Also numbers whose first differences of 0-prepended prime indices have median 0.
%F A360558 A001222(a(n)) > 2*A001221(a(n)).
%e A360558 The terms together with their prime indices begin:
%e A360558      8: {1,1,1}
%e A360558     16: {1,1,1,1}
%e A360558     27: {2,2,2}
%e A360558     32: {1,1,1,1,1}
%e A360558     48: {1,1,1,1,2}
%e A360558     64: {1,1,1,1,1,1}
%e A360558     72: {1,1,1,2,2}
%e A360558     80: {1,1,1,1,3}
%e A360558     81: {2,2,2,2}
%e A360558     96: {1,1,1,1,1,2}
%e A360558    108: {1,1,2,2,2}
%e A360558    112: {1,1,1,1,4}
%e A360558    125: {3,3,3}
%e A360558 For example, the prime indices of 720 are {1,1,1,1,2,2,3} with 4 adjacent equalities and 3 distinct parts, so 720 is in the sequence.
%t A360558 Select[Range[100],PrimeOmega[#]>2*PrimeNu[#]&]
%Y A360558 For equality we have A067801.
%Y A360558 These partitions are counted by A360254.
%Y A360558 A112798 lists prime indices, length A001222, sum A056239.
%Y A360558 A326567/A326568 gives mean of prime indices.
%Y A360558 A360005 gives median of prime indices (times 2).
%Y A360558 Cf. A000975, A027193, A067340, A237363, A317090, A360248, A360249, A360454, A360555, A360556.
%K A360558 nonn
%O A360558 1,1
%A A360558 _Gus Wiseman_, Feb 20 2023