A333966 Positive integers where the number of triples of divisors (d1, d2, d3) such that d1 < d2 < d3 < 2*d1 and each pair of these divisors is pairwise coprime, sets a new record.
1, 60, 280, 420, 840, 1260, 2520, 6930, 9240, 13860, 27720, 55440, 60060, 120120, 180180, 240240, 360360, 720720, 1021020, 1801800, 2042040, 2282280, 2762760, 3063060, 4084080, 4564560, 6126120, 12252240, 19399380, 24504480, 30630600, 36756720, 38798760, 58198140, 77597520
Offset: 1
Keywords
Examples
280 has two such divisor triples; (4, 5, 7) and (5, 7, 8) and no number less than 280 has at least two such triples so 280 is in the sequence.
Links
- David A. Corneth, records; number of such triples in divisors of a(n)
Programs
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PARI
upto(n) = { v = vectorsmall(n); for(i = 2, sqrtnint(n, 3), for(j = i + 1, min(sqrtint(n \ i), 2*i-2), g = gcd(i, j); if(g == 1, l = i * j / g; for(k = j + 1, min(2*i-1, n \ (i*j)), if(gcd(l, k) == 1, p = l*k; forstep(m = p, n, p, v[m]++ ); t++ ))))); my(res=List(1), r=v[1]); for(i=2, #v, if(v[i]>r, r=v[i]; listput(res,i))); res }
Comments