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A326848 Heinz numbers of integer partitions of m >= 0 whose length times maximum is a multiple of m.

%I A326848 #5 Jul 29 2019 13:55:37
%S A326848 1,2,3,4,5,7,8,9,11,13,16,17,19,23,25,27,28,29,31,32,37,40,41,43,47,
%T A326848 49,53,59,61,64,67,71,73,78,79,81,83,84,89,97,101,103,107,109,113,121,
%U A326848 125,127,128,131,137,139,149,151,157,163,167,169,171,173,179,181
%N A326848 Heinz numbers of integer partitions of m >= 0 whose length times maximum is a multiple of m.
%C A326848 The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%C A326848 The enumeration of these partitions by sum is given by A326849.
%e A326848 The sequence of terms together with their prime indices begins:
%e A326848     1: {}
%e A326848     2: {1}
%e A326848     3: {2}
%e A326848     4: {1,1}
%e A326848     5: {3}
%e A326848     7: {4}
%e A326848     8: {1,1,1}
%e A326848     9: {2,2}
%e A326848    11: {5}
%e A326848    13: {6}
%e A326848    16: {1,1,1,1}
%e A326848    17: {7}
%e A326848    19: {8}
%e A326848    23: {9}
%e A326848    25: {3,3}
%e A326848    27: {2,2,2}
%e A326848    28: {1,1,4}
%e A326848    29: {10}
%e A326848    31: {11}
%e A326848    32: {1,1,1,1,1}
%e A326848    37: {12}
%t A326848 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A326848 Select[Range[100],#==1||Divisible[Max[primeMS[#]]*Length[primeMS[#]],Total[primeMS[#]]]&]
%Y A326848 Cf. A001222, A047993, A056239, A061395, A067538, A112798, A316413, A326836, A326843, A326847, A326849, A326851.
%K A326848 nonn
%O A326848 1,2
%A A326848 _Gus Wiseman_, Jul 26 2019