A362606 Numbers without a unique least prime exponent, or numbers whose prime factorization has more than one element of least multiplicity.

6, 10, 14, 15, 21, 22, 26, 30, 33, 34, 35, 36, 38, 39, 42, 46, 51, 55, 57, 58, 60, 62, 65, 66, 69, 70, 74, 77, 78, 82, 84, 85, 86, 87, 90, 91, 93, 94, 95, 100, 102, 105, 106, 110, 111, 114, 115, 118, 119, 120, 122, 123, 126, 129, 130, 132, 133, 134, 138, 140

Offset

1,1

Comments

First differs from A130092 in lacking 180.

First differs from A351295 in lacking 180 and having 216.

First differs from A362605 in having 60.

Links

Table of n, a(n) for n=1..60.

Example

The prime factorization of 1800 is {2,2,2,3,3,5,5}, and the parts of least multiplicity are {3,5}, so 1800 is in the sequence.
The terms together with their prime indices begin:
    6: {1,2}
   10: {1,3}
   14: {1,4}
   15: {2,3}
   21: {2,4}
   22: {1,5}
   26: {1,6}
   30: {1,2,3}
   33: {2,5}
   34: {1,7}
   35: {3,4}
   36: {1,1,2,2}
   38: {1,8}
   39: {2,6}
   42: {1,2,4}

Mathematica

Select[Range[100], Count[Last/@FactorInteger[#], Min@@Last/@FactorInteger[#]]>1&]

Crossrefs

The complement is A359178, counted by A362610.

For mode we have A362605, counted by A362607.

Partitions of this type are counted by A362609.

These are the positions of terms > 1 in A362613.

A112798 lists prime indices, length A001222, sum A056239.

A362614 counts partitions by number of modes.

A362615 counts partitions by number of co-modes.

Cf. A215366, A327473, A327476, A353864, A356862, A359908, A362611.

Sequence in context: A279458 A119899 A351295 * A130092 A289619 A329140

Adjacent sequences: A362603 A362604 A362605 * A362607 A362608 A362609

Keyword

nonn

Author

Gus Wiseman, May 05 2023

Status

approved