A390988 Numbers k > 1 such that the least prime index of k plus the greatest prime index of k is odd.

6, 12, 14, 15, 18, 24, 26, 28, 33, 35, 36, 38, 42, 45, 48, 51, 52, 54, 56, 58, 65, 69, 70, 72, 74, 75, 76, 77, 78, 84, 86, 93, 95, 96, 98, 99, 104, 106, 108, 112, 114, 116, 119, 122, 123, 126, 130, 135, 140, 141, 142, 143, 144, 145, 148, 152, 153, 156, 158

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..59.

Example

The terms together with their prime indices begin:
   6: {1,2}
  12: {1,1,2}
  14: {1,4}
  15: {2,3}
  18: {1,2,2}
  24: {1,1,1,2}
  26: {1,6}
  28: {1,1,4}
  33: {2,5}
  35: {3,4}
  36: {1,1,2,2}
  38: {1,8}
  42: {1,2,4}
  45: {2,2,3}
  48: {1,1,1,1,2}

Mathematica

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

Crossrefs

For odd A001222(n) we have A026424, counted by A027193, strict A067659.

For greatest prime index odd we have A244991, counted by A027193, strict A026837.

For odd sum of all prime indices we have A300063, counted by A058695.

For just the least prime index odd we have A340932, counted by A026804, strict A026832.

Partitions of this type are counted by A390092, strict A390746.

For product instead of sum we have A390093, counted by A325338, strict A391228.

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

The complement is A391226.

A028260 lists numbers with even bigomega, counted by A027187, strict A067661.

A055396 and A061395 select least and greatest prime index.

A066207 = numbers whose prime indices are all even, counted by A035363, strict A035457.

A066208 = numbers whose prime indices are all odd, counted by A000009, strict A000700.

A112798 lists the prime indices of each positive integer, row sums A056239.

A257991 counts odd prime indices.

Cf. A006141, A005408, A026805, A031368, A160786, A300272, A324522, A340604, A340854, A340855, A340933, A341446.

Sequence in context: A318981 A105115 A366532 * A325700 A360551 A306999

Adjacent sequences: A390985 A390986 A390987 * A390989 A390990 A390991

Keyword

nonn

Author

Gus Wiseman, Nov 29 2025

Status

approved