cp's OEIS Frontend

A363949 Numbers whose prime indices have mean 1 when rounded down.

%I A363949 #6 Jul 02 2023 22:32:04
%S A363949 2,4,6,8,12,16,18,20,24,32,36,40,48,54,56,60,64,72,80,96,108,112,120,
%T A363949 128,144,160,162,168,176,180,192,200,216,224,240,256,288,320,324,336,
%U A363949 352,360,384,400,416,432,448,480,486,504,512,528,540,560,576,600,640
%N A363949 Numbers whose prime indices have mean 1 when rounded down.
%C A363949 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 A363949 a(n) = 2*A344296(n).
%e A363949 The terms together with their prime indices begin:
%e A363949     2: {1}
%e A363949     4: {1,1}
%e A363949     6: {1,2}
%e A363949     8: {1,1,1}
%e A363949    12: {1,1,2}
%e A363949    16: {1,1,1,1}
%e A363949    18: {1,2,2}
%e A363949    20: {1,1,3}
%e A363949    24: {1,1,1,2}
%e A363949    32: {1,1,1,1,1}
%e A363949    36: {1,1,2,2}
%e A363949    40: {1,1,1,3}
%e A363949    48: {1,1,1,1,2}
%e A363949    54: {1,2,2,2}
%e A363949    56: {1,1,1,4}
%e A363949    60: {1,1,2,3}
%e A363949    64: {1,1,1,1,1,1}
%t A363949 prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A363949 Select[Range[100],Floor[Mean[prix[#]]]==1&]
%Y A363949 These partitions are counted by A025065.
%Y A363949 Before rounding down we had A326567/A326568.
%Y A363949 For mode instead of mean we have A360015, counted by A241131.
%Y A363949 For median instead of mean we have A363488, counted by A027336.
%Y A363949 Positions of 1's in A363943, triangle A363945.
%Y A363949 For the usual rounding (not low or high) we have A363948, counted by A363947.
%Y A363949 A112798 lists prime indices, length A001222, sum A056239.
%Y A363949 A316413 ranks partitions with integer mean, counted by A067538.
%Y A363949 A360005 gives twice the median of prime indices.
%Y A363949 A363941 gives low median of prime indices, triangle A124943.
%Y A363949 A363942 gives high median of prime indices, triangle A124944.
%Y A363949 For mean 2 instead of 1 we have A363950, counted by A026905 redoubled.
%Y A363949 Cf. A051293, A327473, A327476, A344296, A359889, A360013, A363723, A363727, A363946, A363951.
%K A363949 nonn
%O A363949 1,1
%A A363949 _Gus Wiseman_, Jul 02 2023