A362606 - OEIS

%I #5 May 06 2023 09:03:02

%S 6,10,14,15,21,22,26,30,33,34,35,36,38,39,42,46,51,55,57,58,60,62,65,

%T 66,69,70,74,77,78,82,84,85,86,87,90,91,93,94,95,100,102,105,106,110,

%U 111,114,115,118,119,120,122,123,126,129,130,132,133,134,138,140

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

%C First differs from A130092 in lacking 180.

%C First differs from A351295 in lacking 180 and having 216.

%C First differs from A362605 in having 60.

%e 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.

%e The terms together with their prime indices begin:

%e     6: {1,2}

%e    10: {1,3}

%e    14: {1,4}

%e    15: {2,3}

%e    21: {2,4}

%e    22: {1,5}

%e    26: {1,6}

%e    30: {1,2,3}

%e    33: {2,5}

%e    34: {1,7}

%e    35: {3,4}

%e    36: {1,1,2,2}

%e    38: {1,8}

%e    39: {2,6}

%e    42: {1,2,4}

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

%Y The complement is A359178, counted by A362610.

%Y For mode we have A362605, counted by A362607.

%Y Partitions of this type are counted by A362609.

%Y These are the positions of terms > 1 in A362613.

%Y A112798 lists prime indices, length A001222, sum A056239.

%Y A362614 counts partitions by number of modes.

%Y A362615 counts partitions by number of co-modes.

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

%K nonn

%O 1,1

%A _Gus Wiseman_, May 05 2023