A303283 - OEIS

%I #6 Apr 21 2018 20:58:27

%S 42,78,105,114,130,174,182,195,210,222,230,231,258,266,285,318,345,

%T 357,366,370,390,406,426,429,435,455,462,470,474,483,494,518,534,546,

%U 555,570,598,602,606,610,627,638,642,645,651,663,665,678,690,705,714,715

%N Squarefree numbers whose prime indices have no common divisor other than 1 but are not pairwise coprime.

%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.

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

%e The sequence of strict integer partitions whose Heinz numbers belong to this sequence begins (4,2,1), (6,2,1), (4,3,2), (8,2,1), (6,3,1), (10,2,1), (6,4,1), (6,3,2), (4,3,2,1), (12,2,1), (9,3,1), (5,4,2), (14,2,1), (8,4,1), (8,3,2), (16,2,1), (9,3,2), (7,4,2), (18,2,1), (12,3,1), (6,3,2,1).

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

%t Select[Range[400],SquareFreeQ[#]&&!CoprimeQ@@primeMS[#]&&GCD@@primeMS[#]===1&]

%Y Cf. A000837, A001222, A018783, A051424, A056239, A078374, A168532, A289508, A289509, A296150, A298748, A300486, A302569, A302696, A302796, A303138, A303139, A303140, A303282.

%K nonn

%O 1,1

%A _Gus Wiseman_, Apr 20 2018