cp's OEIS Frontend

A302798 Squarefree numbers that are prime or whose prime indices are pairwise coprime. Heinz numbers of strict integer partitions that either consist of a single part or have pairwise coprime parts.

%I A302798 #5 Apr 13 2018 21:54:54
%S A302798 1,2,3,5,6,7,10,11,13,14,15,17,19,22,23,26,29,30,31,33,34,35,37,38,41,
%T A302798 43,46,47,51,53,55,58,59,61,62,66,67,69,70,71,73,74,77,79,82,83,85,86,
%U A302798 89,93,94,95,97,101,102,103,106,107,109,110,113,118,119,122
%N A302798 Squarefree numbers that are prime or whose prime indices are pairwise coprime. Heinz numbers of strict integer partitions that either consist of a single part or have pairwise coprime parts.
%C A302798 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 A302798 The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%e A302798 Sequence of terms together with their sets of prime indices begins:
%e A302798 01 : {}
%e A302798 02 : {1}
%e A302798 03 : {2}
%e A302798 05 : {3}
%e A302798 06 : {1,2}
%e A302798 07 : {4}
%e A302798 10 : {1,3}
%e A302798 11 : {5}
%e A302798 13 : {6}
%e A302798 14 : {1,4}
%e A302798 15 : {2,3}
%e A302798 17 : {7}
%e A302798 19 : {8}
%e A302798 22 : {1,5}
%e A302798 23 : {9}
%e A302798 26 : {1,6}
%e A302798 29 : {10}
%e A302798 30 : {1,2,3}
%t A302798 Select[Range[100],Or[#===1,SquareFreeQ[#]&&(PrimeQ[#]||CoprimeQ@@PrimePi/@FactorInteger[#][[All,1]])]&]
%Y A302798 Cf. A001222, A003963, A005117, A007359, A051424, A056239, A275024, A289509, A294472, A302242, A302505, A302696, A302697, A302698, A302796, A302797.
%K A302798 nonn
%O A302798 1,2
%A A302798 _Gus Wiseman_, Apr 13 2018