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

1,2

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).

Links

Table of n, a(n) for n=1..64.

Example

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}

Mathematica

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

Crossrefs

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

Sequence in context: A167171 A087008 A326537 * A294472 A077337 A093501

Adjacent sequences: A302795 A302796 A302797 * A302799 A302800 A302801

Keyword

nonn

Author

Gus Wiseman, Apr 13 2018

Status

approved