cp's OEIS Frontend

A366319 Numbers k such that the sum of prime indices of k is not twice the maximum prime index of k, meaning A056239(k) != 2 * A061395(k).

%I A366319 #7 Oct 10 2023 09:31:07
%S A366319 1,2,3,5,6,7,8,10,11,13,14,15,16,17,18,19,20,21,22,23,24,26,27,28,29,
%T A366319 31,32,33,34,35,36,37,38,39,41,42,43,44,45,46,47,48,50,51,52,53,54,55,
%U A366319 56,57,58,59,60,61,62,64,65,66,67,68,69,71,72,73,74,75,76
%N A366319 Numbers k such that the sum of prime indices of k is not twice the maximum prime index of k, meaning A056239(k) != 2 * A061395(k).
%C A366319 A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
%C A366319 Also Heinz numbers of integer partitions containing n/2, where n is the sum of all parts.
%e A366319 The prime indices of 90 are {1,2,2,3}, with sum 8 and twice maximum 6, so 90 is in the sequence.
%t A366319 prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A366319 Select[Range[100],Max[prix[#]]!=Total[prix[#]]/2&]
%Y A366319 Partitions of this type are counted by A086543.
%Y A366319 For length instead of maximum we have the complement of A340387.
%Y A366319 The complement is A344415, counted by A035363.
%Y A366319 A001221 counts distinct prime factors, A001222 with multiplicity.
%Y A366319 A056239 adds up prime indices, row sums of A112798.
%Y A366319 A334201 adds up all prime indices except the greatest.
%Y A366319 A344291 lists numbers m with A001222(m) <= A056239(m)/2, counted by A110618.
%Y A366319 A344296 lists numbers m with A001222(m) >= A056239(m)/2, counted by A025065.
%Y A366319 Cf. A001414, A100959, A238628, A300061, A301987, A316413, A320924, A344414, A344416, A366318.
%K A366319 nonn
%O A366319 1,2
%A A366319 _Gus Wiseman_, Oct 10 2023