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 A242492 For any integer m > 1, the m-th term of the sequence is the minimal squarefree integer x with exactly m prime divisors such that x+1 and x+2 are also squarefree integers with exactly m prime divisors. 2
 33, 1309, 203433, 16467033, 1990586013, 41704979953, 102099792179229 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS The five terms for m = 2,3,4,5,6 were computed with the aid of PARI/GP. But it seems to be rather difficult to compute higher terms, if they exist at all. The distribution of squarefree integers with exactly m prime factors is given in the book by Montgomery and Vaughan, Multiplicative Number Theory, but I do not have access to it and do not know whether it also addresses the problem of three consecutive numbers of this kind. REFERENCES Hugh L. Montgomery and Robert C. Vaughan: "Multiplicative Number Theory: 1. Classical Theory", Cambridge studies in advanced mathematics, vol. 97, Cambridge University Press (2007) LINKS Math Overflow, Asymptotics of special square-free numbers, Mar 20 2014 Daniel Constantin Mayer, PARI/GP script "AdjacentSquareFree.gp" Daniel Constantin Mayer, PARI/GP script "SquareFreeTriplets.gp" Prime puzzles & problems connection, Square-free triples FORMULA a(n) = A093550(n)-1. - M. F. Hasler, May 20 2014 EXAMPLE 33 = 3*11, 34 = 2*17, 35 = 5*7; 1309 = 7*11*17, 1310 = 2*5*131, 1311 = 3*19*23; 203433 = 3*19*43*83, 203434 = 2*7*11*1321, 203435 = 5*23*29*61; 16467033 = 3*11*17*149*197, 16467034 = 2*19*23*83*227, 16467035 = 5*13*37*41*167; (CPU time 48 seconds) 1990586013 = 3*13*29*67*109*241, 1990586014 = 2*23*37*43*59*461, 1990586015 = 5*11*17*19*89*1259. (CPU time 2 hours and 34 minutes) PROG (PARI) {default(primelimit, 2M); lb=2; ub=2*10^9; m=1; i=0; j=0; loc=0; while(m<6, m=m+1; for(n=lb, ub, if(issquarefree(n)&&(m==omega(n)), loc=loc+1; if(1==loc, i=n; ); if(2==loc, if(i+1==n, j=n; ); if(i+1

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Last modified July 3 10:20 EDT 2020. Contains 335417 sequences. (Running on oeis4.)