A199970 a(n) = the smallest number m with the smallest non-divisor n such that 1<n<m, or 0 if no such m exists.

0, 3, 4, 6, 12, 0, 60, 420, 840, 0, 2520, 0, 27720, 0, 0, 360360, 720720, 0, 12252240, 0, 0, 0, 232792560, 0, 5354228880, 0, 26771144400, 0, 80313433200, 0, 2329089562800, 72201776446800, 0, 0, 0, 0, 144403552893600, 0, 0, 0, 5342931457063200, 0, 219060189739591200

Offset

1,2

Links

Table of n, a(n) for n=1..43.

Formula

a(n) > 0 for prime powers n = p^k (p prime, k >= 1) else 0.

a(n) = A003418(n-1) for n = p^k > 3 (p prime, k >= 1). - Amiram Eldar, Aug 06 2024

Example

 a(7) = 60 because 60 is the smallest number such that numbers k < 7 divides 60 but number 7 is not divisor of 60.

Mathematica

a[n_] := If[PrimePowerQ[n], If[n <= 3, n+1, LCM @@ Range[n-1]], 0]; Array[a, 50] (* Amiram Eldar, Aug 06 2024 *)

Crossrefs

Cf. A003418, A199968, A199969.

Sequence in context: A192813 A048229 A002090 * A283738 A366535 A368469

Adjacent sequences: A199967 A199968 A199969 * A199971 A199972 A199973

Keyword

nonn

Author

Jaroslav Krizek, Nov 26 2011

Extensions

More terms from Amiram Eldar, Aug 06 2024

Status

approved