cp's OEIS Frontend

A322552 MM-numbers of triangles.

%I A322552 #19 Dec 29 2018 13:02:44
%S A322552 17719,40807,140699,185803,219271,421031,511219,570011,588787,897689,
%T A322552 916777,1321433,1581827,1654823,1769609,1854983,2028181,2358773,
%U A322552 2456737,2943343,3641501,3705221,3890389,3902981,4186793,4807489,5176613,5263759,5693197,6308857,6515111,6566717
%N A322552 MM-numbers of triangles.
%C A322552 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}}.
%C A322552 Sequence consists of terms of the form prime(p*q) * prime(p*r) * prime(q*r), with p, q, and r distinct primes. - _Charlie Neder_, Dec 23 2018
%H A322552 David A. Corneth, <a href="/A322552/b322552.txt">Table of n, a(n) for n = 1..12878</a> (first 900 terms from Charlie Neder)
%e A322552 The sequence of triangles whose MM-numbers belong to the sequence begins:
%e A322552    17719: {{1,2},{1,3},{2,3}}
%e A322552    40807: {{1,2},{1,4},{2,4}}
%e A322552   140699: {{1,2},{1,5},{2,5}}
%e A322552   185803: {{1,3},{1,4},{3,4}}
%e A322552   219271: {{1,2},{1,6},{2,6}}
%e A322552   421031: {{1,2},{1,7},{2,7}}
%e A322552   511219: {{2,3},{2,4},{3,4}}
%e A322552   570011: {{1,2},{1,8},{2,8}}
%e A322552   588787: {{1,3},{1,5},{3,5}}
%e A322552   897689: {{1,2},{1,9},{2,9}}
%e A322552   916777: {{1,3},{1,6},{3,6}}
%t A322552 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A322552 Select[Range[100000],And[SquareFreeQ[#],PrimeOmega[#]==3,And@@(SquareFreeQ[#]&&PrimeOmega[#]==2&/@primeMS[#]),SameQ[##,2]&@@Length/@Split[Sort[Join@@primeMS/@primeMS[#]]]]&]
%Y A322552 Cf. A001222, A001358, A003963, A006881, A056239, A106349, A112798, A302242, A305078, A320458, A320635, A322551.
%K A322552 nonn,easy
%O A322552 1,1
%A A322552 _Gus Wiseman_, Dec 15 2018
%E A322552 a(12)-a(32) from _Charlie Neder_, Dec 27 2018