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Smallest number whose product of digits equals n!.
3

%I #18 Dec 21 2015 17:15:32

%S 1,1,2,6,38,358,2589,25789,257889,2578879,45578899

%N Smallest number whose product of digits equals n!.

%C The sequence is finite because n! for n>10 has 2-digit prime factors.

%e For n=4 the solutions having digit products equal 24 excluding those with digit 1 are: {38, 46, 64, 83, 226, 234, 243, 262, 324, 342, 423, 432, 622, 2223, 2232, 2322, 3222} of which the smallest is 38. For n>1, numbers with a digit 1 are too big.

%Y Cf. A000142, A001222, A002473, A067734, A068183-A068187, A068189-A068191.

%K base,fini,nonn,full

%O 0,3

%A _Labos Elemer_, Feb 18 2002

%E Edited by _Henry Bottomley_, Feb 26 2002