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%I #5 Apr 01 2019 07:25:06
%S 1,3,4,5,7,8,11,13,15,16,17,19,21,23,25,27,29,31,32,33,35,37,39,41,43,
%T 47,49,51,53,55,57,59,61,64,65,67,69,71,73,77,79,81,83,85,87,89,91,93,
%U 95,97,100,101,103,105,107,109,111,113,115,119,121,123,127
%N Heinz numbers of integer partitions where the set of distinct parts is disjoint from the set of distinct multiplicities.
%C The enumeration of these partitions by sum is given by A114639.
%C The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k), so these are numbers where the prime indices are disjoint from the prime exponents.
%e The sequence of terms together with their prime indices begins:
%e 1: {}
%e 3: {2}
%e 4: {1,1}
%e 5: {3}
%e 7: {4}
%e 8: {1,1,1}
%e 11: {5}
%e 13: {6}
%e 15: {2,3}
%e 16: {1,1,1,1}
%e 17: {7}
%e 19: {8}
%e 21: {2,4}
%e 23: {9}
%e 25: {3,3}
%e 27: {2,2,2}
%e 29: {10}
%e 31: {11}
%e 32: {1,1,1,1,1}
%e 33: {2,5}
%t Select[Range[100],Intersection[PrimePi/@First/@FactorInteger[#],Last/@FactorInteger[#]]=={}&]
%Y Cf. A000720, A001222, A056239, A109298, A112798, A114639, A118914.
%Y Cf. A324571, A325127, A325128, A325129, A325130.
%K nonn
%O 1,2
%A _Gus Wiseman_, Apr 01 2019
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