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%I #6 Jul 27 2019 14:57:51
%S 1,2,3,5,6,7,11,13,14,17,19,21,23,26,29,31,33,35,37,38,41,42,43,47,53,
%T 57,58,59,61,67,69,71,73,74,79,83,86,89,95,97,101,103,106,107,109,111,
%U 113,114,122,123,127,131,133,137,139,142,149,151,157,158,159
%N Heinz numbers of strict integer partitions with no binary carries.
%C A binary carry of two positive integers is an overlap of the positions of 1's in their reversed binary expansion.
%C The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1) * ... * prime(y_k), so these are squarefree numbers whose prime indices have no carries. 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.
%e The sequence of terms together with their prime indices begins:
%e 1: {}
%e 2: {1}
%e 3: {2}
%e 5: {3}
%e 6: {1,2}
%e 7: {4}
%e 11: {5}
%e 13: {6}
%e 14: {1,4}
%e 17: {7}
%e 19: {8}
%e 21: {2,4}
%e 23: {9}
%e 26: {1,6}
%e 29: {10}
%e 31: {11}
%e 33: {2,5}
%e 35: {3,4}
%e 37: {12}
%e 38: {1,8}
%e 41: {13}
%e 42: {1,2,4}
%t binpos[n_]:=Join@@Position[Reverse[IntegerDigits[n,2]],1];
%t stableQ[u_,Q_]:=!Apply[Or,Outer[#1=!=#2&&Q[#1,#2]&,u,u,1],{0,1}];
%t Select[Range[100],SquareFreeQ[#]&&stableQ[PrimePi/@First/@FactorInteger[#],Intersection[binpos[#1],binpos[#2]]!={}&]&]
%Y Cf. A050315, A056239, A080572, A112798, A247935, A267610.
%Y Cf. A325095, A325096, A325097, A325100, A325101, A325103, A325110, A325119.
%K nonn
%O 1,2
%A _Gus Wiseman_, Mar 28 2019
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