cp's OEIS Frontend

A382856 Numbers whose prime indices do not have a mode of 1.

%I A382856 #9 Apr 07 2025 09:26:41
%S A382856 1,3,5,7,9,11,13,15,17,18,19,21,23,25,27,29,31,33,35,37,39,41,43,45,
%T A382856 47,49,50,51,53,54,55,57,59,61,63,65,67,69,71,73,75,77,79,81,83,85,87,
%U A382856 89,90,91,93,95,97,98,99,101,103,105,107,108,109,111,113,115
%N A382856 Numbers whose prime indices do not have a mode of 1.
%e A382856 The terms together with their prime indices begin:
%e A382856    1: {}
%e A382856    3: {2}
%e A382856    5: {3}
%e A382856    7: {4}
%e A382856    9: {2,2}
%e A382856   11: {5}
%e A382856   13: {6}
%e A382856   15: {2,3}
%e A382856   17: {7}
%e A382856   18: {1,2,2}
%e A382856   19: {8}
%e A382856   21: {2,4}
%e A382856   23: {9}
%e A382856   25: {3,3}
%e A382856   27: {2,2,2}
%t A382856 prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A382856 Select[Range[100],FreeQ[Commonest[prix[#]],1]&]
%Y A382856 The case of non-unique mode is A024556.
%Y A382856 The complement is A360015 except first.
%Y A382856 Partitions of this type are are counted by A382526 except first, complement A241131.
%Y A382856 A091602 counts partitions by the greatest multiplicity, rank statistic A051903.
%Y A382856 A112798 lists prime indices, length A001222, sum A056239.
%Y A382856 A116598 counts ones in partitions, rank statistic A007814.
%Y A382856 A240312 counts partitions with max part = max multiplicity, ranks A381542.
%Y A382856 A362611 counts modes in prime indices, triangle A362614.
%Y A382856 For co-mode see A359178, A362613, A364061 (A364062), A364158 (A364159).
%Y A382856 Cf. A000265, A002865, A106529, A327473, A327476, A362605, A363486, A356862, A360013, A360014, A381437.
%K A382856 nonn
%O A382856 1,2
%A A382856 _Gus Wiseman_, Apr 07 2025