OFFSET
1,2
COMMENTS
Records are 0, 1, 2, 3, 4, 5, 8, 9, 11, 13, 19, ...
Are terms > 4564560 products of primorials (cf. A025487)? Terms 4564560 < k <= 54765047434897800 are.
In a triple (d1, d2, d3) such that lcm(d1, d2, d3) = d1*d2*d2 <= k we must have d1^3 < k. Proof: Suppose d1^3 >= n. Then d1 * d2 * d3 > n since d2 > d1 and d3 > d1. Since any pair is coprime d1 * d2 * d3 = LCM(d1,d2,d3) is a divisor of n. A contradiction. - David A. Corneth and Amiram Eldar, Jul 28 2020
LINKS
EXAMPLE
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.
PROG
(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 }
CROSSREFS
KEYWORD
nonn
AUTHOR
David A. Corneth, Jul 22 2020
STATUS
approved