cp's OEIS Frontend

A320456 Numbers whose multiset multisystem spans an initial interval of positive integers.

%I A320456 #5 Oct 15 2018 22:20:52
%S A320456 1,2,3,4,6,7,8,9,12,13,14,15,16,18,19,21,24,26,27,28,30,32,35,36,37,
%T A320456 38,39,42,45,48,49,52,53,54,56,57,60,61,63,64,65,69,70,72,74,75,76,78,
%U A320456 81,84,89,90,91,95,96,98,104,105,106,108,111,112,113,114,117
%N A320456 Numbers whose multiset multisystem spans an initial interval of positive integers.
%C A320456 A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798. The n-th multiset multisystem is formed by taking the multiset of prime indices of each part of the multiset of prime indices of n. For example, the prime indices of 78 are {1,2,6}, so the 78th multiset multisystem is {{},{1},{1,2}}.
%e A320456 The sequence of terms together with their multiset multisystems begins:
%e A320456    1: {}
%e A320456    2: {{}}
%e A320456    3: {{1}}
%e A320456    4: {{},{}}
%e A320456    6: {{},{1}}
%e A320456    7: {{1,1}}
%e A320456    8: {{},{},{}}
%e A320456    9: {{1},{1}}
%e A320456   12: {{},{},{1}}
%e A320456   13: {{1,2}}
%e A320456   14: {{},{1,1}}
%e A320456   15: {{1},{2}}
%e A320456   16: {{},{},{},{}}
%e A320456   18: {{},{1},{1}}
%e A320456   19: {{1,1,1}}
%e A320456   21: {{1},{1,1}}
%e A320456   24: {{},{},{},{1}}
%e A320456   26: {{},{1,2}}
%e A320456   27: {{1},{1},{1}}
%e A320456   28: {{},{},{1,1}}
%e A320456   30: {{},{1},{2}}
%e A320456   32: {{},{},{},{},{}}
%t A320456 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A320456 normQ[sys_]:=Or[Length[sys]==0,Union@@sys==Range[Max@@Max@@sys]];
%t A320456 Select[Range[100],normQ[primeMS/@primeMS[#]]&]
%Y A320456 Cf. A001222, A003963, A034691, A034729, A055932, A056239, A112798, A255906, A290103, A302242, A305052.
%Y A320456 Cf. A320458, A320459, A320461, A320462, A320463, A320464, A320532, A320533.
%K A320456 nonn
%O A320456 1,2
%A A320456 _Gus Wiseman_, Oct 13 2018