cp's OEIS Frontend

A325031 Numbers divisible by all prime indices of their prime indices.

%I A325031 #5 Mar 26 2019 21:05:15
%S A325031 1,2,3,4,6,7,8,9,10,12,14,16,18,19,20,21,24,26,27,28,30,32,33,36,38,
%T A325031 40,42,46,48,49,50,52,53,54,56,57,60,63,64,66,68,70,72,74,76,78,80,81,
%U A325031 84,87,90,92,96,98,99,100,104,106,108,112,114,120,122,126,128
%N A325031 Numbers divisible by all prime indices of their prime indices.
%C A325031 A prime index of n is a number m such that prime(m) divides n. For example, the prime indices of 55 are {3,5} with prime indices {{2},{3}}. Since 55 is not divisible by 2 or 3, it does not belong to the sequence.
%e A325031 The sequence of multisets of multisets whose MM-numbers (see A302242) belong to the sequence begins:
%e A325031    1: {}
%e A325031    2: {{}}
%e A325031    3: {{1}}
%e A325031    4: {{},{}}
%e A325031    6: {{},{1}}
%e A325031    7: {{1,1}}
%e A325031    8: {{},{},{}}
%e A325031    9: {{1},{1}}
%e A325031   10: {{},{2}}
%e A325031   12: {{},{},{1}}
%e A325031   14: {{},{1,1}}
%e A325031   16: {{},{},{},{}}
%e A325031   18: {{},{1},{1}}
%e A325031   19: {{1,1,1}}
%e A325031   20: {{},{},{2}}
%e A325031   21: {{1},{1,1}}
%e A325031   24: {{},{},{},{1}}
%e A325031   26: {{},{1,2}}
%e A325031   27: {{1},{1},{1}}
%e A325031   28: {{},{},{1,1}}
%e A325031   30: {{},{1},{2}}
%e A325031   32: {{},{},{},{},{}}
%e A325031   33: {{1},{3}}
%e A325031   36: {{},{},{1},{1}}
%t A325031 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A325031 Select[Range[100],And@@Table[Divisible[#,i],{i,Union@@primeMS/@primeMS[#]}]&]
%Y A325031 Cf. A000720, A003963, A112798, A120383, A302242, A320325.
%Y A325031 Cf. A323440, A324846, A324847, A324849, A324850, A324856, A324926, A325032.
%K A325031 nonn
%O A325031 1,2
%A A325031 _Gus Wiseman_, Mar 25 2019