A304713 - OEIS

%I #4 May 17 2018 21:37:05

%S 1,2,3,5,7,11,13,15,17,19,23,29,31,33,35,37,41,43,47,51,53,55,59,61,

%T 67,69,71,73,77,79,83,85,89,91,93,95,97,101,103,107,109,113,119,123,

%U 127,131,137,139,141,143,145,149,151,155,157,161,163,165,167,173

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

%C A prime index of n is a number m such that prime(m) divides n. The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).

%e Sequence of entries together with their corresponding multiset multisystems (see A302242) begins:

%e 1:  {}

%e 2:  {{}}

%e 3:  {{1}}

%e 5:  {{2}}

%e 7:  {{1,1}}

%e 11: {{3}}

%e 13: {{1,2}}

%e 15: {{1},{2}}

%e 17: {{4}}

%e 19: {{1,1,1}}

%e 23: {{2,2}}

%e 29: {{1,3}}

%e 31: {{5}}

%e 33: {{1},{3}}

%e 35: {{2},{1,1}}

%t Select[Range[300],SquareFreeQ[#]&&Select[Tuples[PrimePi/@First/@FactorInteger[#],2],UnsameQ@@#&&Divisible@@#&]==={}&]

%Y Cf. A000009, A005117, A006126, A056239, A073576, A285572, A285573, A293606, A293993, A302696, A302796, A303362, A303365, A304711.

%K nonn

%O 1,2

%A _Gus Wiseman_, May 17 2018