A302478 Products of prime numbers of squarefree index.

1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 20, 22, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 36, 39, 40, 41, 43, 44, 45, 47, 48, 50, 51, 52, 54, 55, 58, 59, 60, 62, 64, 65, 66, 67, 68, 72, 73, 75, 78, 79, 80, 81, 82, 83, 85, 86, 87, 88, 90, 93, 94

Offset: 1

Author

Gus Wiseman, Apr 08 2018

Keywords

• nonn

Comments

A prime index of n is a number m such that prime(m) divides n.

Examples

			Entry A302242 describes a correspondence between positive integers and multiset multisystems. In this case it gives the following sequence of set multisystems.
01:  {}
02:  {{}}
03:  {{1}}
04:  {{},{}}
05:  {{2}}
06:  {{},{1}}
08:  {{},{},{}}
09:  {{1},{1}}
10:  {{},{2}}
11:  {{3}}
12:  {{},{},{1}}
13:  {{1,2}}
15:  {{1},{2}}
16:  {{},{},{},{}}
17:  {{4}}
18:  {{},{1},{1}}
20:  {{},{},{2}}
22:  {{},{3}}
24:  {{},{},{},{1}}
25:  {{2},{2}}
26:  {{},{1,2}}
27:  {{1},{1},{1}}
29:  {{1,3}}
30:  {{},{1},{2}}
31:  {{5}}
32:  {{},{},{},{},{}}
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000961, A001222, A003963, A005117, A007716, A050320, A056239, A063834, A076610, A270995, A275024, A281113, A296119, A301753, A302242, A302243, A302491.

Programs

Mathematica

Select[Range[100],Or[#===1,And@@SquareFreeQ/@PrimePi/@FactorInteger[#][[All,1]]]&]

PARI

ok(n)={!#select(p->!issquarefree(primepi(p)), factor(n)[,1])} \\ Andrew Howroyd, Aug 26 2018