A304713 Squarefree numbers whose prime indices are pairwise indivisible. Heinz numbers of strict integer partitions with pairwise indivisible parts.

1, 2, 3, 5, 7, 11, 13, 15, 17, 19, 23, 29, 31, 33, 35, 37, 41, 43, 47, 51, 53, 55, 59, 61, 67, 69, 71, 73, 77, 79, 83, 85, 89, 91, 93, 95, 97, 101, 103, 107, 109, 113, 119, 123, 127, 131, 137, 139, 141, 143, 145, 149, 151, 155, 157, 161, 163, 165, 167, 173

Offset

1,2

Comments

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).

Links

Table of n, a(n) for n=1..60.

Example

Sequence of entries together with their corresponding multiset multisystems (see A302242) begins:
1:  {}
2:  {{}}
3:  {{1}}
5:  {{2}}
7:  {{1,1}}
11: {{3}}
13: {{1,2}}
15: {{1},{2}}
17: {{4}}
19: {{1,1,1}}
23: {{2,2}}
29: {{1,3}}
31: {{5}}
33: {{1},{3}}
35: {{2},{1,1}}

Mathematica

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

Crossrefs

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

Sequence in context: A102553 A069161 A328603 * A319327 A319319 A003277

Adjacent sequences: A304710 A304711 A304712 * A304714 A304715 A304716

Keyword

nonn

Author

Gus Wiseman, May 17 2018

Status

approved