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A322552
MM-numbers of triangles.
1
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[#]]]]&]
KEYWORD
nonn,easy
AUTHOR
Gus Wiseman, Dec 15 2018
EXTENSIONS
a(12)-a(32) from Charlie Neder, Dec 27 2018
STATUS
approved