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A046148 Number of n-digit numbers with maximal multiplicative persistence A014553. 3
10, 1, 9, 12, 20, 2430, 5229, 7448, 282852, 88200, 8015040, 200676960, 2701775518, 24655323238, 15765750, 1715313600, 59049874884, 1112489914536, 14162129381400, 135917876094000, 1050596838951660, 6832549561749912, 38554260751029408, 193081920969057120 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Giovanni Resta, Table of n, a(n) for n = 1..50

N. J. A. Sloane, The persistence of a number, J. Recreational Math., 6 (1973), 97-98.

Eric Weisstein's World of Mathematics, Multiplicative Persistence.

MATHEMATICA

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 *)

CROSSREFS

Cf. A014553, A046149, A046150.

Sequence in context: A010184 A107830 A144261 * A231933 A164915 A010691

Adjacent sequences:  A046145 A046146 A046147 * A046149 A046150 A046151

KEYWORD

nonn,base

AUTHOR

Eric W. Weisstein

EXTENSIONS

a(8)-a(12) from Donovan Johnson, Mar 30 2010

a(13)-a(24) from Giovanni Resta, Aug 31 2018

STATUS

approved

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Last modified February 20 17:04 EST 2020. Contains 332080 sequences. (Running on oeis4.)