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%I A362606 #5 May 06 2023 09:03:02
%S A362606 6,10,14,15,21,22,26,30,33,34,35,36,38,39,42,46,51,55,57,58,60,62,65,
%T A362606 66,69,70,74,77,78,82,84,85,86,87,90,91,93,94,95,100,102,105,106,110,
%U A362606 111,114,115,118,119,120,122,123,126,129,130,132,133,134,138,140
%N A362606 Numbers without a unique least prime exponent, or numbers whose prime factorization has more than one element of least multiplicity.
%C A362606 First differs from A130092 in lacking 180.
%C A362606 First differs from A351295 in lacking 180 and having 216.
%C A362606 First differs from A362605 in having 60.
%e A362606 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 A362606 The terms together with their prime indices begin:
%e A362606     6: {1,2}
%e A362606    10: {1,3}
%e A362606    14: {1,4}
%e A362606    15: {2,3}
%e A362606    21: {2,4}
%e A362606    22: {1,5}
%e A362606    26: {1,6}
%e A362606    30: {1,2,3}
%e A362606    33: {2,5}
%e A362606    34: {1,7}
%e A362606    35: {3,4}
%e A362606    36: {1,1,2,2}
%e A362606    38: {1,8}
%e A362606    39: {2,6}
%e A362606    42: {1,2,4}
%t A362606 Select[Range[100],Count[Last/@FactorInteger[#],Min@@Last/@FactorInteger[#]]>1&]
%Y A362606 The complement is A359178, counted by A362610.
%Y A362606 For mode we have A362605, counted by A362607.
%Y A362606 Partitions of this type are counted by A362609.
%Y A362606 These are the positions of terms > 1 in A362613.
%Y A362606 A112798 lists prime indices, length A001222, sum A056239.
%Y A362606 A362614 counts partitions by number of modes.
%Y A362606 A362615 counts partitions by number of co-modes.
%Y A362606 Cf. A215366, A327473, A327476, A353864, A356862, A359908, A362611.
%K A362606 nonn
%O A362606 1,1
%A A362606 _Gus Wiseman_, May 05 2023

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