A391226 Numbers k > 1 such that the least prime index of k plus the greatest prime index of k is even.

2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 16, 17, 19, 20, 21, 22, 23, 25, 27, 29, 30, 31, 32, 34, 37, 39, 40, 41, 43, 44, 46, 47, 49, 50, 53, 55, 57, 59, 60, 61, 62, 63, 64, 66, 67, 68, 71, 73, 79, 80, 81, 82, 83, 85, 87, 88, 89, 90, 91, 92, 94, 97, 100, 101, 102, 103

Offset

1,1

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..66.

Example

The terms together with their prime indices begin:
    2: {1}
    3: {2}
    4: {1,1}
    5: {3}
    7: {4}
    8: {1,1,1}
    9: {2,2}
   10: {1,3}
   11: {5}
   13: {6}
   16: {1,1,1,1}
   17: {7}
   19: {8}
   20: {1,1,3}
   21: {2,4}
   22: {1,5}
   23: {9}
   25: {3,3}
   27: {2,2,2}
   29: {10}
   30: {1,2,3}

Mathematica

prix[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[2, 100], EvenQ[First[prix[#]]+Last[prix[#]]]&]

Crossrefs

The case where all prime indices are even is A066207, counted by A035363.

For greatest prime index even we have A244990, counted by A027187, strict A067661.

For even sum of prime indices we have A300061, counted by A058696.

For even least prime index we have A340933, counted by A026805, strict A026833.

The complement is A390988, counted by A390092, strict A390746.

These are positions of even terms in A390430, for differences A243055.

Partitions of this type are counted by A391225, strict A391227.

For product instead of sum we have A391229, counted by A391230, strict A391231.

Cf. A026424, A026804, A027193, A066208, A244991, A300063, A325338, A340932, A390093, A391228.

Sequence in context: A014122 A324759 A360550 * A326621 A324758 A305504

Adjacent sequences: A391223 A391224 A391225 * A391227 A391228 A391229

Keyword

nonn

Author

Gus Wiseman, Dec 06 2025

Status

approved