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%I #6 Mar 18 2019 08:14:17
%S 1,2,3,4,5,7,8,9,10,11,13,16,17,19,20,21,22,23,25,27,29,31,32,33,34,
%T 35,37,40,41,43,44,46,47,49,50,51,53,57,59,61,62,63,64,65,67,68,71,73,
%U 77,79,80,81,82,83,85,87,88,89,91,92,93,94,95,97,99,100,101
%N Heinz numbers of integer partitions containing no prime indices of the parts.
%C 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. The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
%C These could be described as anti-transitive numbers (cf. A290822), as they are numbers x such that if prime(y) divides x and prime(z) divides y, then prime(z) does not divide x.
%C Also numbers n such that A003963(n) is coprime to n.
%e The sequence of terms together with their prime indices begins:
%e 1: {}
%e 2: {1}
%e 3: {2}
%e 4: {1,1}
%e 5: {3}
%e 7: {4}
%e 8: {1,1,1}
%e 9: {2,2}
%e 10: {1,3}
%e 11: {5}
%e 13: {6}
%e 16: {1,1,1,1}
%e 17: {7}
%e 19: {8}
%e 20: {1,1,3}
%e 21: {2,4}
%e 22: {1,5}
%e 23: {9}
%e 25: {3,3}
%e 27: {2,2,2}
%t primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t Select[Range[100],Intersection[primeMS[#],Union@@primeMS/@primeMS[#]]=={}&]
%Y The subset version is A324741, with maximal case A324743. The strict integer partition version is A324751. The integer partition version is A324756. An infinite version is A324695.
%Y Cf. A000720, A001221, A001462, A007097, A056239, A112798, A276625, A289509, A290822, A304360, A306844, A324742, A324753, A324764.
%K nonn
%O 1,2
%A _Gus Wiseman_, Mar 17 2019
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