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%I #29 Aug 06 2024 02:23:02
%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.
%H Robert Israel, <a href="/A333965/b333965.txt">Table of n, a(n) for n = 1..1064</a>
%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.
%p f:= proc(p) local t,k;
%p t:= 1;
%p for k from 1 do
%p t:= t*p;
%p if nops(convert(convert(t,base,10),set))=10 then return k fi;
%p od
%p end proc:
%p R:= NULL: m:= 0: p:= 1: count:= 0:
%p for k from 1 while count < 100 do
%p p:= nextprime(p);
%p v:= k*f(p);
%p if v > m then
%p R:= R,k;
%p m:= v;
%p count:= count+1
%p fi
%p od:
%p R; # _Robert Israel_, Aug 05 2024
%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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