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%I #36 Sep 29 2023 18:32:22
%S 1,4,9,16,36,100,144,324,400,576,900,1764,2304,3600,7056,8100,14400,
%T 28224,32400,44100,57600,108900,112896,129600,176400,396900,435600,
%U 518400,608400,705600,1587600,2822400,5336100,6350400,14288400,15681600,17640000,21344400
%N Numbers m where A217854(m) is a record minimum.
%C (-m)^tau(m) < 0 and (-m)^tau(m) < (-k)^tau(k) for all positive k < m, where tau is the number of divisors function.
%C All terms are squares.
%C It is conjectured that if m is a term, then abs((-m)^tau(m)) <= abs((-k)^tau(k)) for some k < m. See the link.
%H Simon K. Jensen, <a href="https://www.simonjensen.com/pdf/On_an_extended_divisor_product_summatory_function.pdf">On an extended divisor product summatory function</a>
%e 9 is a term since (-9)^tau(9) = (-9)^3 = -729 and -729 < (-k)^tau(k) for k = 1,...,8.
%e 25 is not a term since (-25)^tau(5) = (-25)^3 = -15625 > (-16)^tau(16) = (-16)^5 = -1048576 and 16 < 25.
%o (PARI) isok(m) = my(x=(-m)^numdiv(m)); for (k=1, m-1, if (x >= (-k)^numdiv(k), return(0))); return(1); \\ _Michel Marcus_, Jun 18 2023
%Y Cf. A363658, A000290, A067128, A000005, A217854, A224914.
%K nonn
%O 1,2
%A _Simon Jensen_, Jun 13 2023
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