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

Author

Gus Wiseman, May 05 2023

Keywords

• nonn

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.

Examples

			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}
		

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.

Programs

Mathematica

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