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Odd numbers whose prime indices are relatively prime. Heinz numbers of integer partitions with no 1's and with relatively prime parts.
20

%I #14 Apr 13 2018 07:44:42

%S 15,33,35,45,51,55,69,75,77,85,93,95,99,105,119,123,135,141,143,145,

%T 153,155,161,165,175,177,187,195,201,205,207,209,215,217,219,221,225,

%U 231,245,249,253,255,265,275,279,285,287,291,295,297,309,315,323,327,329

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

%C A prime index of n is a number m such that prime(m) divides n.

%C The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).

%e Sequence of integer partitions with no 1's and with relatively prime parts begins:

%e 015: (3,2)

%e 033: (5,2)

%e 035: (4,3)

%e 045: (3,2,2)

%e 051: (7,2)

%e 055: (5,3)

%e 069: (9,2)

%e 075: (3,3,2)

%e 077: (5,4)

%e 085: (7,3)

%e 093: (11,2)

%e 095: (8,3)

%e 099: (5,2,2)

%e 105: (4,3,2)

%e 119: (7,4)

%e 123: (13,2)

%e 135: (3,2,2,2)

%t primeMS[n_]:=If[n===1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];

%t Select[Range[1,200,2],GCD@@primeMS[#]===1&]

%Y Cf. A000837, A000961, A001222, A005117, A007359, A051424, A076078, A101268, A275024, A285572, A289509, A298748, A302568, A302569, A302696, A302698.

%K nonn

%O 1,1

%A _Gus Wiseman_, Apr 11 2018