A360008 - OEIS

%I #6 Jan 24 2023 12:35:36

%S 1,3,5,6,7,11,12,13,14,17,18,19,23,24,26,29,31,37,38,41,42,43,47,48,

%T 52,53,54,58,59,61,67,71,72,73,74,76,79,83,86,89,92,96,97,101,103,104,

%U 106,107,108,109,113,122,124,127,131,137,139,142,148,149,151,152

%N Positions of first appearances in the sequence giving the mean of prime indices (A326567/A326568).

%C 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 The terms together with their prime indices begin:

%e     1: {}

%e     3: {2}

%e     5: {3}

%e     6: {1,2}

%e     7: {4}

%e    11: {5}

%e    12: {1,1,2}

%e    13: {6}

%e    14: {1,4}

%e    17: {7}

%e    18: {1,2,2}

%e    19: {8}

%e    23: {9}

%e    24: {1,1,1,2}

%t nn=1000;

%t prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];

%t seq=Table[If[n==1,1,Mean[prix[n]]],{n,nn}];

%t Select[Range[nn],FreeQ[seq[[Range[#-1]]],seq[[#]]]&]

%Y Positions of first appearances in A326567/A326568.

%Y The version for median instead of mean is A360007, unsorted A360006.

%Y A058398 counts partitions by mean, see also A008284, A327482.

%Y A112798 lists prime indices, length A001222, sum A056239.

%Y A316413 lists numbers whose prime indices have integer mean.

%Y A326567/A326568 gives mean of prime indices.

%Y A359908 = numbers w/ integer median of prime indices, complement A359912.

%Y Cf. A026424, A051293, A327473, A348551, A359889, A360005.

%K nonn

%O 1,2

%A _Gus Wiseman_, Jan 24 2023