cp's OEIS Frontend

A319877 Numbers whose product of prime indices (A003963) is a square of a squarefree number (A062503).

%I A319877 #40 Dec 18 2018 17:07:15
%S A319877 1,7,9,14,18,23,25,28,36,46,50,56,72,92,97,100,112,121,144,151,161,
%T A319877 169,175,183,184,185,194,195,200,207,224,225,227,242,288,289,302,322,
%U A319877 338,350,366,368,370,388,390,400,414,448,450,454,484,541,576,578,604,644
%N A319877 Numbers whose product of prime indices (A003963) is a square of a squarefree number (A062503).
%C A319877 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 multiset multisystem with MM-number n 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 multiset multisystem with MM-number 78 is {{},{1},{1,2}}. This sequence lists all MM-numbers of 2-regular multiset multisystems (meaning all vertex-degrees are 2).
%e A319877 The sequence of multiset multisystems whose MM-numbers belong to the sequence begins:
%e A319877     1: {}
%e A319877     7: {{1,1}}
%e A319877     9: {{1},{1}}
%e A319877    14: {{},{1,1}}
%e A319877    18: {{},{1},{1}}
%e A319877    23: {{2,2}}
%e A319877    25: {{2},{2}}
%e A319877    28: {{},{},{1,1}}
%e A319877    36: {{},{},{1},{1}}
%e A319877    46: {{},{2,2}}
%e A319877    50: {{},{2},{2}}
%e A319877    56: {{},{},{},{1,1}}
%e A319877    72: {{},{},{},{1},{1}}
%e A319877    92: {{},{},{2,2}}
%e A319877    97: {{3,3}}
%e A319877   100: {{},{},{2},{2}}
%e A319877   112: {{},{},{},{},{1,1}}
%e A319877   121: {{3},{3}}
%e A319877   144: {{},{},{},{},{1},{1}}
%e A319877   151: {{1,1,2,2}}
%e A319877   161: {{1,1},{2,2}}
%e A319877   169: {{1,2},{1,2}}
%e A319877   175: {{2},{2},{1,1}}
%e A319877   183: {{1},{1,2,2}}
%e A319877   184: {{},{},{},{2,2}}
%e A319877   185: {{2},{1,1,2}}
%e A319877   194: {{},{3,3}}
%e A319877   195: {{1},{2},{1,2}}
%e A319877   200: {{},{},{},{2},{2}}
%t A319877 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A319877 Select[Range[100],Or[#==1,SameQ[##,2]&@@Last/@FactorInteger[Times@@primeMS[#]]]&]
%Y A319877 Cf. A003963, A005117, A005176, A062503, A064573, A072774, A295193, A302505, A319878, A319899, A320325, A322526, A322527, A322530.
%K A319877 nonn
%O A319877 1,2
%A A319877 _Gus Wiseman_, Dec 17 2018