A379146 Numbers k that are not in A378930 (i.e., are never the value of f(n) = n * d(n) / gcd(n, d(n))^2, where d = A000005).

18, 27, 45, 63, 64, 72, 99, 112, 117, 144, 153, 160, 171, 207, 225, 243, 252, 261, 279, 288, 320, 333, 336, 352, 360, 369, 387, 396, 416, 423, 441, 468, 477, 504, 531, 544, 549, 567, 576, 603, 608, 612, 616, 625, 639, 657, 684, 711, 728, 736, 747, 792, 801, 828, 873, 880, 891, 909, 927, 928, 936, 952, 963, 981, 992

Offset: 1

Author

Viliam Furík, Dec 16 2024

Keywords

• nonn

Comments

Verified using the known values of f(n) up to a limit determined by the upper bound for divisor function 2*sqrt(n). The lower bound for f(n) is n/d(n), which can be combined with d(n) <= 2*sqrt(n) to yield f(n) >= sqrt(n)/2, and n <= 4*f(n)^2. E.g. for f(n) = 18, this means that checking f(n) for n <= 1296 is sufficient to verify it's never the value of f(n).

It appears that all numbers 9*p, p prime, are in this sequence.

Links

• Viliam Furík, Table of n, a(n) for n = 1..13935

Crossrefs

Cf. A000005. Complement of A378930.