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Squarefree numbers whose prime indices are pairwise coprime. Heinz numbers of strict integer partitions with pairwise coprime parts.
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%I #5 Apr 13 2018 21:54:46

%S 1,2,6,10,14,15,22,26,30,33,34,35,38,46,51,55,58,62,66,69,70,74,77,82,

%T 85,86,93,94,95,102,106,110,118,119,122,123,134,138,141,142,143,145,

%U 146,154,155,158,161,165,166,170,177,178,186,187,190,194,201,202

%N Squarefree numbers whose prime indices are pairwise coprime. Heinz numbers of strict integer partitions with pairwise coprime parts.

%C A prime index of n is a number m such that prime(m) divides n. Two or more numbers are coprime if no pair of them has a common divisor other than 1. A single number is not considered coprime unless it is equal to 1.

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

%e Sequence of terms together with their sets of prime indices begins:

%e 01 : {}

%e 02 : {1}

%e 06 : {1,2}

%e 10 : {1,3}

%e 14 : {1,4}

%e 15 : {2,3}

%e 22 : {1,5}

%e 26 : {1,6}

%e 30 : {1,2,3}

%e 33 : {2,5}

%e 34 : {1,7}

%e 35 : {3,4}

%e 38 : {1,8}

%e 46 : {1,9}

%e 51 : {2,7}

%e 55 : {3,5}

%e 58 : {1,10}

%e 62 : {1,11}

%e 66 : {1,2,5}

%e 69 : {2,9}

%e 70 : {1,3,4}

%t Select[Range[100],Or[#===1,SquareFreeQ[#]&&CoprimeQ@@PrimePi/@FactorInteger[#][[All,1]]]&]

%Y Cf. A001222, A003963, A005117, A007359, A051424, A056239, A275024, A289509, A302242, A302505, A302696, A302697, A302698, A302796, A302798.

%K nonn

%O 1,2

%A _Gus Wiseman_, Apr 13 2018