A322552 MM-numbers of triangles.

17719, 40807, 140699, 185803, 219271, 421031, 511219, 570011, 588787, 897689, 916777, 1321433, 1581827, 1654823, 1769609, 1854983, 2028181, 2358773, 2456737, 2943343, 3641501, 3705221, 3890389, 3902981, 4186793, 4807489, 5176613, 5263759, 5693197, 6308857, 6515111, 6566717

Offset: 1

Author

Gus Wiseman, Dec 15 2018

Keywords

• nonn
• easy

Comments

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}}.

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

Examples

			The sequence of triangles whose MM-numbers belong to the sequence begins:
   17719: {{1,2},{1,3},{2,3}}
   40807: {{1,2},{1,4},{2,4}}
  140699: {{1,2},{1,5},{2,5}}
  185803: {{1,3},{1,4},{3,4}}
  219271: {{1,2},{1,6},{2,6}}
  421031: {{1,2},{1,7},{2,7}}
  511219: {{2,3},{2,4},{3,4}}
  570011: {{1,2},{1,8},{2,8}}
  588787: {{1,3},{1,5},{3,5}}
  897689: {{1,2},{1,9},{2,9}}
  916777: {{1,3},{1,6},{3,6}}
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..12878 (first 900 terms from Charlie Neder)

Crossrefs

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

Programs

Mathematica

primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
Select[Range[100000],And[SquareFreeQ[#],PrimeOmega[#]==3,And@@(SquareFreeQ[#]&&PrimeOmega[#]==2&/@primeMS[#]),SameQ[##,2]&@@Length/@Split[Sort[Join@@primeMS/@primeMS[#]]]]&]

Extensions

a(12)-a(32) from Charlie Neder, Dec 27 2018