A302478 - OEIS

%I #10 Aug 27 2018 01:52:57

%S 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,

%T 32,33,34,36,39,40,41,43,44,45,47,48,50,51,52,54,55,58,59,60,62,64,65,

%U 66,67,68,72,73,75,78,79,80,81,82,83,85,86,87,88,90,93,94

%N Products of prime numbers of squarefree index.

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

%H Andrew Howroyd, <a href="/A302478/b302478.txt">Table of n, a(n) for n = 1..1000</a>

%e Entry A302242 describes a correspondence between positive integers and multiset multisystems. In this case it gives the following sequence of set multisystems.

%e 01:  {}

%e 02:  {{}}

%e 03:  {{1}}

%e 04:  {{},{}}

%e 05:  {{2}}

%e 06:  {{},{1}}

%e 08:  {{},{},{}}

%e 09:  {{1},{1}}

%e 10:  {{},{2}}

%e 11:  {{3}}

%e 12:  {{},{},{1}}

%e 13:  {{1,2}}

%e 15:  {{1},{2}}

%e 16:  {{},{},{},{}}

%e 17:  {{4}}

%e 18:  {{},{1},{1}}

%e 20:  {{},{},{2}}

%e 22:  {{},{3}}

%e 24:  {{},{},{},{1}}

%e 25:  {{2},{2}}

%e 26:  {{},{1,2}}

%e 27:  {{1},{1},{1}}

%e 29:  {{1,3}}

%e 30:  {{},{1},{2}}

%e 31:  {{5}}

%e 32:  {{},{},{},{},{}}

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

%o (PARI) ok(n)={!#select(p->!issquarefree(primepi(p)), factor(n)[,1])} \\ _Andrew Howroyd_, Aug 26 2018

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

%K nonn

%O 1,2

%A _Gus Wiseman_, Apr 08 2018