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

1,1

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

Links

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

Example

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}}

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[#]]]]&]

Crossrefs

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

Sequence in context: A252624 A252513 A328868 * A235023 A133540 A237776

Adjacent sequences: A322549 A322550 A322551 * A322553 A322554 A322555

Keyword

nonn,easy

Author

Gus Wiseman, Dec 15 2018

Extensions

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

Status

approved