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%I #12 Aug 26 2019 18:45:44
%S 0,1,1,2,2,3,4,4,4,6,5,6,8,9,8,10,9,12,12,10,12,15,16,14,16,18,16,20,
%T 18,21,20,20,24,25,20,22,24,28,25,30,27,30,32,27,30,35,36,36,33,36,35,
%U 40,40,42,36,36,40,45,36,42,48,49,48,50,45,48,48,54,50
%N a(n) is the greatest product of the digits of n in any base b in the range 2..n.
%H Rémy Sigrist, <a href="/A309965/b309965.txt">Table of n, a(n) for n = 2..10000</a>
%H Rémy Sigrist, <a href="/A309965/a309965.png">Scatterplot of (n, n-a(n)) for n = 2..50000</a>
%F a(n) < n.
%e For n = 8:
%e - the digits of 8 in bases b = 2..8 and the corresponding products are:
%e b digits product
%e - ------ -------
%e 2 "1000" 0
%e 3 "22" 4
%e 4 "20" 0
%e 5 "13" 3
%e 6 "12" 2
%e 7 "11" 1
%e 8 "10" 0
%e - hence a(8) = 4.
%o (PARI) a(n) = vecmax(vector(n-1, b, vecprod(digits(n,b+1))))
%Y See A309969 for the corresponding base b.
%Y Cf. A007954.
%K nonn,base
%O 2,4
%A _Rémy Sigrist_, Aug 25 2019