A328674 Numbers whose distinct prime indices have no consecutive divisible parts.

1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 15, 16, 17, 19, 23, 25, 27, 29, 31, 32, 33, 35, 37, 41, 43, 45, 47, 49, 51, 53, 55, 59, 61, 64, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 113, 119, 121, 123, 125, 127, 128, 131, 135

Offset

1,2

Comments

First differs from A316476 in having 105, with prime indices {2, 3, 4}.

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..64.

Example

The sequence of terms together with their prime indices begins:
    1: {}
    2: {1}
    3: {2}
    4: {1,1}
    5: {3}
    7: {4}
    8: {1,1,1}
    9: {2,2}
   11: {5}
   13: {6}
   15: {2,3}
   16: {1,1,1,1}
   17: {7}
   19: {8}
   23: {9}
   25: {3,3}
   27: {2,2,2}
   29: {10}
   31: {11}
   32: {1,1,1,1,1}
For example, 45 is in the sequence because its distinct prime indices are {2,3} and 2 is not a divisor of 3.

Mathematica

Select[Range[100], !MatchQ[PrimePi/@First/@FactorInteger[#], {___, x_, y_, ___}/; Divisible[y, x]]&]

Crossrefs

These are the Heinz numbers of the partitions counted by A328675.

The strict version is A328603.

Partitions without consecutive divisibilities are A328171.

Compositions without consecutive divisibilities are A328460.

Cf. A056239, A112798, A316476, A318729, A328335, A328336, A328593, A328598.

Sequence in context: A115405 A343857 A257144 * A316476 A056867 A320324

Adjacent sequences: A328671 A328672 A328673 * A328675 A328676 A328677

Keyword

nonn

Author

Gus Wiseman, Oct 29 2019

Status

approved