cp's OEIS Frontend

A326836 Heinz numbers of integer partitions whose maximum part divides their sum.

%I A326836 #5 Jul 29 2019 13:54:28
%S A326836 2,3,4,5,7,8,9,11,12,13,16,17,19,23,25,27,29,30,31,32,36,37,40,41,43,
%T A326836 47,48,49,53,59,61,63,64,67,70,71,73,79,81,83,84,89,97,101,103,107,
%U A326836 108,109,112,113,121,125,127,128,131,135,137,139,144,149,150,151
%N A326836 Heinz numbers of integer partitions whose maximum part divides their sum.
%C A326836 The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k), so these are numbers whose maximum prime index divides their sum of prime indices.
%C A326836 The enumeration of these partitions by sum is given by A067538.
%e A326836 The sequence of terms together with their prime indices begins:
%e A326836     2: {1}
%e A326836     3: {2}
%e A326836     4: {1,1}
%e A326836     5: {3}
%e A326836     7: {4}
%e A326836     8: {1,1,1}
%e A326836     9: {2,2}
%e A326836    11: {5}
%e A326836    12: {1,1,2}
%e A326836    13: {6}
%e A326836    16: {1,1,1,1}
%e A326836    17: {7}
%e A326836    19: {8}
%e A326836    23: {9}
%e A326836    25: {3,3}
%e A326836    27: {2,2,2}
%e A326836    29: {10}
%e A326836    30: {1,2,3}
%e A326836    31: {11}
%e A326836    32: {1,1,1,1,1}
%t A326836 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A326836 Select[Range[200],Divisible[Total[primeMS[#]],Max[primeMS[#]]]&]
%Y A326836 Cf. A018818, A047993, A056239, A061395, A067538, A112798, A316413.
%Y A326836 Cf. A326837, A326838, A326839/A326840, A326841, A326843, A326850.
%K A326836 nonn
%O A326836 1,1
%A A326836 _Gus Wiseman_, Jul 26 2019