A382769 Largest k < n such that gcd(k,n) > 1 and rad(k) does not divide n, where rad = A007947, or 0 if k does not exist.

0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 10, 0, 12, 12, 0, 0, 15, 0, 18, 18, 20, 0, 22, 0, 24, 0, 26, 0, 28, 0, 0, 30, 30, 30, 34, 0, 36, 36, 38, 0, 40, 0, 42, 42, 44, 0, 46, 0, 48, 48, 50, 0, 52, 50, 54, 54, 56, 0, 58, 0, 60, 60, 0, 60, 63, 0, 66, 66, 68, 0, 70, 0, 72

Offset: 1

Author

Michael De Vlieger, Apr 04 2025

Keywords

• nonn
• easy

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000961, A024619, A096014, A272619.

Programs

Mathematica

rad[x_] := rad[x] = Times @@ FactorInteger[x][[All, 1]]; {0}~Join~Table[If[Nor[PrimePowerQ[n], n == 6], k = n - 2; While[Or[CoprimeQ[n, k], Divisible[n, rad[k]]], k--]; k, 0], {n, 2, 120}]

Formula

a(n) = 0 for n = 6, and n in A000961.

For n > 6 in A024619, a(n) is the last term in row n of A272619.