A328336 Numbers with no consecutive prime indices relatively prime.

1, 2, 3, 5, 7, 9, 11, 13, 17, 19, 21, 23, 25, 27, 29, 31, 37, 39, 41, 43, 47, 49, 53, 57, 59, 61, 63, 65, 67, 71, 73, 79, 81, 83, 87, 89, 91, 97, 101, 103, 107, 109, 111, 113, 115, 117, 121, 125, 127, 129, 131, 133, 137, 139, 147, 149, 151, 157, 159, 163, 167

Offset

1,2

Comments

First differs from A318978 in having 897, with prime indices {2, 6, 9}.

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.

The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k), so these are Heinz numbers of partitions no consecutive parts relatively prime (A328187).

Besides the initial 1 this differs from A305078: 47541=897*prime(16) is in A305078 but not in this set. - Andrey Zabolotskiy, Nov 13 2019

Links

Table of n, a(n) for n=1..61.

Example

The sequence of terms together with their prime indices begins:
   1: {}
   2: {1}
   3: {2}
   5: {3}
   7: {4}
   9: {2,2}
  11: {5}
  13: {6}
  17: {7}
  19: {8}
  21: {2,4}
  23: {9}
  25: {3,3}
  27: {2,2,2}
  29: {10}
  31: {11}
  37: {12}
  39: {2,6}
  41: {13}
  43: {14}

Mathematica

primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[100], !MatchQ[primeMS[#], {___, x_, y_, ___}/; GCD[x, y]==1]&]

Crossrefs

Numbers with consecutive prime indices relatively prime are A328335.

Strict partitions with no consecutive parts relatively prime are A328220.

Numbers with relatively prime prime indices are A289509.

Cf. A000837, A056239, A078374, A112798, A281116, A289508, A318981, A328168, A328169, A328172, A328187, A328188.

Sequence in context: A011861 A229511 A305078 * A337694 A305103 A065520

Adjacent sequences: A328333 A328334 A328335 * A328337 A328338 A328339

Keyword

nonn

Author

Gus Wiseman, Oct 14 2019

Status

approved