cp's OEIS Frontend

A360246 Numbers for which the prime indices do not have the same mean as the distinct prime indices.

%I A360246 #8 Feb 08 2023 13:12:01
%S A360246 12,18,20,24,28,40,44,45,48,50,52,54,56,60,63,68,72,75,76,80,84,88,92,
%T A360246 96,98,99,104,108,112,116,117,120,124,126,132,135,136,140,144,147,148,
%U A360246 150,152,153,156,160,162,164,168,171,172,175,176,180,184,188,189
%N A360246 Numbers for which the prime indices do not have the same mean as the distinct prime indices.
%C A360246 First differs from A242416 in having 126.
%C A360246 Contains no squarefree numbers or perfect powers.
%C A360246 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.
%e A360246 The terms together with their prime indices begin:
%e A360246    12: {1,1,2}
%e A360246    18: {1,2,2}
%e A360246    20: {1,1,3}
%e A360246    24: {1,1,1,2}
%e A360246    28: {1,1,4}
%e A360246    40: {1,1,1,3}
%e A360246    44: {1,1,5}
%e A360246    45: {2,2,3}
%e A360246    48: {1,1,1,1,2}
%e A360246    50: {1,3,3}
%e A360246    52: {1,1,6}
%e A360246    54: {1,2,2,2}
%e A360246    56: {1,1,1,4}
%e A360246    60: {1,1,2,3}
%e A360246    63: {2,2,4}
%e A360246    68: {1,1,7}
%e A360246    72: {1,1,1,2,2}
%e A360246 The prime indices of 126 are {1,2,2,4} with mean 9/4 and distinct prime indices {1,2,4} with mean 7/3, so 126 is in the sequence.
%t A360246 prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A360246 Select[Range[100],Mean[prix[#]]!=Mean[Union[prix[#]]]&]
%Y A360246 Signature instead of parts: complement A324570, counted by A114638.
%Y A360246 Signature instead of distinct parts: complement A359903, counted by A360068.
%Y A360246 These partitions are counted by A360242.
%Y A360246 The complement is A360247, counted by A360243.
%Y A360246 For median we have A360248, counted by A360244 (complement A360245).
%Y A360246 Union of A360252 and A360253, counted by A360250 and A360251.
%Y A360246 A058398 counts partitions by mean, also A327482.
%Y A360246 A088529/A088530 gives mean of prime signature (A124010).
%Y A360246 A112798 lists prime indices, length A001222, sum A056239.
%Y A360246 A316413 = numbers whose prime indices have integer mean, distinct A326621.
%Y A360246 A326567/A326568 gives mean of prime indices.
%Y A360246 A326619/A326620 gives mean of distinct prime indices.
%Y A360246 Cf. A000975, A051293, A067340, A067538, A360005, A360241.
%K A360246 nonn
%O A360246 1,1
%A A360246 _Gus Wiseman_, Feb 07 2023