A322552 - OEIS

%I #19 Dec 29 2018 13:02:44

%S 17719,40807,140699,185803,219271,421031,511219,570011,588787,897689,

%T 916777,1321433,1581827,1654823,1769609,1854983,2028181,2358773,

%U 2456737,2943343,3641501,3705221,3890389,3902981,4186793,4807489,5176613,5263759,5693197,6308857,6515111,6566717

%N MM-numbers of triangles.

%C 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 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 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 The sequence of triangles whose MM-numbers belong to the sequence begins:

%e    17719: {{1,2},{1,3},{2,3}}

%e    40807: {{1,2},{1,4},{2,4}}

%e   140699: {{1,2},{1,5},{2,5}}

%e   185803: {{1,3},{1,4},{3,4}}

%e   219271: {{1,2},{1,6},{2,6}}

%e   421031: {{1,2},{1,7},{2,7}}

%e   511219: {{2,3},{2,4},{3,4}}

%e   570011: {{1,2},{1,8},{2,8}}

%e   588787: {{1,3},{1,5},{3,5}}

%e   897689: {{1,2},{1,9},{2,9}}

%e   916777: {{1,3},{1,6},{3,6}}

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

%t Select[Range[100000],And[SquareFreeQ[#],PrimeOmega[#]==3,And@@(SquareFreeQ[#]&&PrimeOmega[#]==2&/@primeMS[#]),SameQ[##,2]&@@Length/@Split[Sort[Join@@primeMS/@primeMS[#]]]]&]

%Y Cf. A001222, A001358, A003963, A006881, A056239, A106349, A112798, A302242, A305078, A320458, A320635, A322551.

%K nonn,easy

%O 1,1

%A _Gus Wiseman_, Dec 15 2018

%E a(12)-a(32) from _Charlie Neder_, Dec 27 2018