cp's OEIS Frontend

A363954 Numbers whose prime indices have low mean 2.

%I A363954 #5 Jul 06 2023 08:55:20
%S A363954 3,9,10,14,15,27,28,30,42,44,45,50,52,63,66,70,75,81,84,88,90,100,104,
%T A363954 126,132,135,136,140,150,152,156,189,196,198,204,208,210,220,225,234,
%U A363954 243,250,252,260,264,270,272,280,294,297,300,304,308,312,315,330,350
%N A363954 Numbers whose prime indices have low mean 2.
%C A363954 Extending the terminology of A124944, the "low mean" of a multiset is obtained by taking the mean and rounding down.
%e A363954 The terms together with their prime indices begin:
%e A363954      3: {2}
%e A363954      9: {2,2}
%e A363954     10: {1,3}
%e A363954     14: {1,4}
%e A363954     15: {2,3}
%e A363954     27: {2,2,2}
%e A363954     28: {1,1,4}
%e A363954     30: {1,2,3}
%e A363954     42: {1,2,4}
%e A363954     44: {1,1,5}
%e A363954     45: {2,2,3}
%e A363954     50: {1,3,3}
%e A363954     52: {1,1,6}
%e A363954     63: {2,2,4}
%e A363954     66: {1,2,5}
%e A363954     70: {1,3,4}
%e A363954     75: {2,3,3}
%e A363954     81: {2,2,2,2}
%e A363954     84: {1,1,2,4}
%e A363954     88: {1,1,1,5}
%e A363954     90: {1,2,2,3}
%e A363954    100: {1,1,3,3}
%t A363954 prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A363954 Select[Range[100],Floor[Mean[prix[#]]]==2&]
%Y A363954 Partitions of this type are counted by A363745.
%Y A363954 Positions of 2's in A363943 (high A363944), triangle A363945 (high A363946).
%Y A363954 For mean 1 we have A363949.
%Y A363954 The high version is A363950, counted by A026905.
%Y A363954 A112798 lists prime indices, length A001222, sum A056239.
%Y A363954 A316413 ranks partitions with integer mean, counted by A067538.
%Y A363954 A326567/A326568 gives mean of prime indices.
%Y A363954 A363941 gives low median of prime indices, triangle A124943.
%Y A363954 A363942 gives high median of prime indices, triangle A124944.
%Y A363954 A363948 lists numbers whose prime indices have mean 1, counted by A363947.
%Y A363954 Cf. A327473, A327476, A359889, A360013, A360015, A363488, A363951.
%K A363954 nonn
%O A363954 1,1
%A A363954 _Gus Wiseman_, Jul 05 2023