This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A363657 #36 Sep 29 2023 18:32:22 %S A363657 1,4,9,16,36,100,144,324,400,576,900,1764,2304,3600,7056,8100,14400, %T A363657 28224,32400,44100,57600,108900,112896,129600,176400,396900,435600, %U A363657 518400,608400,705600,1587600,2822400,5336100,6350400,14288400,15681600,17640000,21344400 %N A363657 Numbers m where A217854(m) is a record minimum. %C A363657 (-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 A363657 All terms are squares. %C A363657 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 A363657 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 A363657 9 is a term since (-9)^tau(9) = (-9)^3 = -729 and -729 < (-k)^tau(k) for k = 1,...,8. %e A363657 25 is not a term since (-25)^tau(5) = (-25)^3 = -15625 > (-16)^tau(16) = (-16)^5 = -1048576 and 16 < 25. %o A363657 (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 A363657 Cf. A363658, A000290, A067128, A000005, A217854, A224914. %K A363657 nonn %O A363657 1,2 %A A363657 _Simon Jensen_, Jun 13 2023