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%I #19 Dec 20 2024 11:54:04
%S 18,27,45,63,64,72,99,112,117,144,153,160,171,207,225,243,252,261,279,
%T 288,320,333,336,352,360,369,387,396,416,423,441,468,477,504,531,544,
%U 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
%N 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).
%C 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).
%C It appears that all numbers 9*p, p prime, are in this sequence.
%H Viliam Furík, <a href="/A379146/b379146.txt">Table of n, a(n) for n = 1..13935</a>
%Y Cf. A000005. Complement of A378930.
%K nonn
%O 1,1
%A _Viliam Furík_, Dec 16 2024