A302594 - OEIS

%I #4 Apr 10 2018 21:49:56

%S 1,2,3,4,5,6,8,9,10,11,12,16,17,18,20,22,24,25,27,31,32,34,36,40,41,

%T 44,48,50,54,59,62,64,67,68,72,80,81,82,83,88,96,100,108,109,118,121,

%U 124,125,127,128,134,136,144,157,160,162,164,166,176,179,191,192

%N Numbers whose prime indices other than 1 are equal prime numbers.

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

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

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

%e 17: {{4}}

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

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

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

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

%t primeMS[n_]:=If[n===1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];

%t Select[Range[400],MatchQ[Union[DeleteCases[primeMS[#],1]],{_?PrimeQ}|{}]&]

%Y Cf. A000961, A001222, A003963, A005117, A006450, A007716, A056239, A076610, A275024, A047968, A281113, A295924, A301760, A302242, A302243.

%K nonn

%O 1,2

%A _Gus Wiseman_, Apr 10 2018