A389879 A005117(k) - 1 where k is the least k such that A389412(k) = n.

2, 1, 4, 12, 56, 540, 64, 32, 280, 460, 28, 756, 2304, 1188, 252, 216, 396, 6732, 900, 792, 2916, 20484, 1332, 2700, 15084, 3384, 3780, 432, 8676, 25776, 323676, 46476, 19800, 4500, 21600, 37800, 19980, 180, 9000, 53676, 43200, 24480, 18180, 262800, 13500, 2376, 302400, 945900

Offset

1,1

Comments

Least number m such that m + A005117(i) is squarefree for 1 <= i <= n, with m + A005117(n+1) nonsquarefree.

Probabilistic arguments (see the Englezou link in A389412) suggest the following conjecture: the set {a(r) : A056170(a(r)) = n} is finite for every n, and the non-unitary prime factors of a(r) are the first n primes.

Links

Miles Englezou, Table of n, a(n) for n = 1..109

Example

3 is the least k such that A389412(k) = 1; A005117(3) - 1 = 2, therefore a(1) = 2.
2 is the least k such that A389412(k) = 2; A005117(2) - 1 = 1, therefore a(2) = 1.
4 is the least k such that A389412(k) = 3; A005117(4) - 1 = 4, therefore a(3) = 4.
9 is the least k such that A389412(k) = 4; A005117(9) - 1 = 12, therefore a(4) = 12.

Prog

(PARI) a(n) = my(f); (f(n) = my(nb = 0); for(r = n, oo, for(m = 1, oo, if(issquarefree(m), if(issquarefree(r - 1 + m), nb++, return(nb)))))); for(k = 2, oo, if(f(k) == n, return(k - 1)))

Crossrefs

Cf. A005117, A056170, A389412.

Sequence in context: A064297 A358501 A323493 * A052661 A225117 A088624

Adjacent sequences: A389876 A389877 A389878 * A389880 A389881 A389882

Keyword

nonn

Author

Miles Englezou, Oct 18 2025

Status

approved