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%I #5 Sep 16 2018 21:36:12
%S 2,5,6,11,14,15,17,23,26,31,33,35,38,41,42,47,51,58,59,65,67,69,73,74,
%T 77,78,83,86,93,95,97,103,105,106,109,110,114,119,122,123,127,137,141,
%U 142,143,145,149,157,158,161,167,170,174,177,178,179,182,185,191
%N Heinz numbers of strict integer partitions of odd numbers. Squarefree numbers whose prime indices sum to an odd number.
%C The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
%e 105 is the Heinz number of (4,3,2), which is strict and has odd weight, so 105 belongs to the sequence.
%e The sequence of all odd-weight strict partitions begins: (1), (3), (2,1), (5), (4,1), (3,2), (7), (9), (6,1), (11), (5,2), (4,3), (8,1), (13), (4,2,1).
%t Select[Range[100],And[SquareFreeQ[#],OddQ[Total[Cases[FactorInteger[#],{p_,k_}:>k*PrimePi[p]]]]]&]
%Y Complement of the union of A319241 and A013929.
%Y Cf. A000041, A000720, A001222, A005117, A008683, A056239, A296150, A299202, A300061, A300063.
%K nonn
%O 1,1
%A _Gus Wiseman_, Sep 15 2018