A046148 - OEIS

%I #16 Sep 01 2018 09:15:32

%S 10,1,9,12,20,2430,5229,7448,282852,88200,8015040,200676960,

%T 2701775518,24655323238,15765750,1715313600,59049874884,1112489914536,

%U 14162129381400,135917876094000,1050596838951660,6832549561749912,38554260751029408,193081920969057120

%N Number of n-digit numbers with maximal multiplicative persistence A014553.

%H Giovanni Resta, <a href="/A046148/b046148.txt">Table of n, a(n) for n = 1..50</a>

%H N. J. A. Sloane, <a href="http://neilsloane.com/doc/persistence.html">The persistence of a number</a>, J. Recreational Math., 6 (1973), 97-98.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MultiplicativePersistence.html">Multiplicative Persistence.</a>

%t mper[n_] := Block[{k=0, m=n}, While[m>9, k++; m = Times @@ IntegerDigits@ m]; k]; mxper = {1, 4, 5, 6, 7, 7, 8, 9, 9, 10, 10, 10}; multi[w_] := Total[w]!/Times @@ (w!); a[1]=10; a[n_] := Sum[ Total[ If[ mxper[[n]] == 1 + mper[Times @@ (Range[9]^#)], multi[#], 0] & /@ Permutations[p]], {p, IntegerPartitions[n, {9}, Range[0, n]]}]; Array[a, 12] (* _Giovanni Resta_, Sep 01 2018 *)

%Y Cf. A014553, A046149, A046150.

%K nonn,base

%O 1,1

%A _Eric W. Weisstein_

%E a(8)-a(12) from _Donovan Johnson_, Mar 30 2010

%E a(13)-a(24) from _Giovanni Resta_, Aug 31 2018