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%I #21 Jan 26 2021 05:57:50
%S 1,2,5,6,8,12,14,16,18,20,25,27,32,43,45,46,52,58,70,71,77,81,91,105,
%T 109,149,158,176,240,247,297,303,401,421,431,531,536,542,543,608,617,
%U 622,640,643,667,677,685,713,720,748,751,1028,1085,1203,1282,1320,1466,1600
%N Numbers k such that k * A171744(k) increases to a record.
%C This sequence shows where A171744(k) is larger than usual around k.
%e 6 is in the sequence as A171744(6) = 22 and 6*22 = 132. This is a record; no n less than 6 produces a product of at least 132.
%t With[{s = Array[Block[{p = Prime@ #, k = 1}, While[Min@ DigitCount[p^k] == 0, k++]; k #] &, 1600]}, Map[FirstPosition[s, #][[1]] &, Union@ FoldList[Max, s]]] (* _Michael De Vlieger_, Aug 21 2020 *)
%o (PARI) f(n) = {my(k=1, p=prime(n)); while(#Set(digits(p^k))<10, k++); k; } \\ A171744
%o lista(nn) = {my(m=0, x); for (n=1, nn, x = n*f(n); if (x >m, m = x; print1(n, ", ")););} \\ _Michel Marcus_, Jan 26 2021
%Y Cf. A171744.
%K nonn,base
%O 1,2
%A _David A. Corneth_, Aug 14 2020
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