A360008 Positions of first appearances in the sequence giving the mean of prime indices (A326567/A326568).

1, 3, 5, 6, 7, 11, 12, 13, 14, 17, 18, 19, 23, 24, 26, 29, 31, 37, 38, 41, 42, 43, 47, 48, 52, 53, 54, 58, 59, 61, 67, 71, 72, 73, 74, 76, 79, 83, 86, 89, 92, 96, 97, 101, 103, 104, 106, 107, 108, 109, 113, 122, 124, 127, 131, 137, 139, 142, 148, 149, 151, 152

Offset

1,2

Comments

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.

Links

Table of n, a(n) for n=1..62.

Example

The terms together with their prime indices begin:
    1: {}
    3: {2}
    5: {3}
    6: {1,2}
    7: {4}
   11: {5}
   12: {1,1,2}
   13: {6}
   14: {1,4}
   17: {7}
   18: {1,2,2}
   19: {8}
   23: {9}
   24: {1,1,1,2}

Mathematica

nn=1000;
prix[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
seq=Table[If[n==1, 1, Mean[prix[n]]], {n, nn}];
Select[Range[nn], FreeQ[seq[[Range[#-1]]], seq[[#]]]&]

Crossrefs

Positions of first appearances in A326567/A326568.

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

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

A112798 lists prime indices, length A001222, sum A056239.

A316413 lists numbers whose prime indices have integer mean.

A326567/A326568 gives mean of prime indices.

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

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

Sequence in context: A129802 A023854 A324511 * A092559 A242076 A349897

Adjacent sequences: A360005 A360006 A360007 * A360009 A360010 A360011

Keyword

nonn

Author

Gus Wiseman, Jan 24 2023

Status

approved