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%I A363658 #41 Sep 01 2023 03:59:34
%S A363658 2,3,5,6,8,10,12,18,20,24,30,40,42,48,60,72,84,90,96,108,120,168,180,
%T A363658 240,336,360,420,480,504,540,600,630,660,672,720,840,1080,1260,1440,
%U A363658 1680,2160,2520,3360,3780,3960,4200,4320,4620,4680,5040,7560,9240,10080
%N A363658 Positive numbers m where A217854(m) is positive and increases to a record.
%C A363658 (-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 A363658 There are no squares in this sequence.
%C A363658 It appears that if n > 13, then a(n) = A067128(n). See the link.
%C A363658 Only a finite number of terms in A002093 can also be terms in this sequence. See the link.
%H A363658 Simon Jensen, <a href="/A363658/b363658.txt">Table of n, a(n) for n = 1..135</a>
%H A363658 Simon 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 A363658 5 is a term since (-5)^tau(5) = (-5)^2 = 25 and 25 > (-k)^tau(k) for k = 1,...,4.
%o A363658 (PARI) isok(m) = my(x=(-m)^numdiv(m)); if (x>0, for (k=1, m-1, if (x <= (-k)^numdiv(k), return(0))); return(1)); \\ _Michel Marcus_, Aug 31 2023
%Y A363658 Cf. A363657, A067128, A000005, A002093, A217854, A224914.
%K A363658 nonn
%O A363658 1,1
%A A363658 _Simon Jensen_, Jun 13 2023

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