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A302697 Odd numbers whose prime indices are relatively prime. Heinz numbers of integer partitions with no 1's and with relatively prime parts.

%I A302697 #14 Apr 13 2018 07:44:42
%S A302697 15,33,35,45,51,55,69,75,77,85,93,95,99,105,119,123,135,141,143,145,
%T A302697 153,155,161,165,175,177,187,195,201,205,207,209,215,217,219,221,225,
%U A302697 231,245,249,253,255,265,275,279,285,287,291,295,297,309,315,323,327,329
%N A302697 Odd numbers whose prime indices are relatively prime. Heinz numbers of integer partitions with no 1's and with relatively prime parts.
%C A302697 A prime index of n is a number m such that prime(m) divides n.
%C A302697 The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%e A302697 Sequence of integer partitions with no 1's and with relatively prime parts begins:
%e A302697 015: (3,2)
%e A302697 033: (5,2)
%e A302697 035: (4,3)
%e A302697 045: (3,2,2)
%e A302697 051: (7,2)
%e A302697 055: (5,3)
%e A302697 069: (9,2)
%e A302697 075: (3,3,2)
%e A302697 077: (5,4)
%e A302697 085: (7,3)
%e A302697 093: (11,2)
%e A302697 095: (8,3)
%e A302697 099: (5,2,2)
%e A302697 105: (4,3,2)
%e A302697 119: (7,4)
%e A302697 123: (13,2)
%e A302697 135: (3,2,2,2)
%t A302697 primeMS[n_]:=If[n===1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A302697 Select[Range[1,200,2],GCD@@primeMS[#]===1&]
%Y A302697 Cf. A000837, A000961, A001222, A005117, A007359, A051424, A076078, A101268, A275024, A285572, A289509, A298748, A302568, A302569, A302696, A302698.
%K A302697 nonn
%O A302697 1,1
%A A302697 _Gus Wiseman_, Apr 11 2018