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.

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, 43, 46, 47, 51, 53, 55, 58, 59, 61, 62, 66, 67, 69, 70, 71, 73, 74, 77, 79, 82, 83, 85, 86, 89, 93, 94, 95, 97, 101, 102, 103, 106, 107, 109, 110, 113, 118, 119, 122

Offset: 1

Author

Gus Wiseman, Apr 13 2018

Keywords

• nonn

Comments

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.

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

Examples

			Sequence of terms together with their sets of prime indices begins:
01 : {}
02 : {1}
03 : {2}
05 : {3}
06 : {1,2}
07 : {4}
10 : {1,3}
11 : {5}
13 : {6}
14 : {1,4}
15 : {2,3}
17 : {7}
19 : {8}
22 : {1,5}
23 : {9}
26 : {1,6}
29 : {10}
30 : {1,2,3}
		

Crossrefs

Cf. A001222, A003963, A005117, A007359, A051424, A056239, A275024, A289509, A294472, A302242, A302505, A302696, A302697, A302698, A302796, A302797.

Programs

Mathematica

Select[Range[100],Or[#===1,SquareFreeQ[#]&&(PrimeQ[#]||CoprimeQ@@PrimePi/@FactorInteger[#][[All,1]])]&]