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A051801
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Product of the nonzero digits of n.
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42
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1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 2, 2, 4, 6, 8, 10, 12, 14, 16, 18, 3, 3, 6, 9, 12, 15, 18, 21, 24, 27, 4, 4, 8, 12, 16, 20, 24, 28, 32, 36, 5, 5, 10, 15, 20, 25, 30, 35, 40, 45, 6, 6, 12, 18, 24, 30, 36, 42, 48, 54, 7, 7, 14, 21
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graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = 1 if n=0, otherwise a(floor(n/10)) * (n mod 10 + 0^(n mod 10)). - Reinhard Zumkeller, Oct 13 2009
G.f. A(x) satisfies: A(x) = (1 + x + 2*x^2 + 3*x^3 + 4*x^4 + 5*x^5 + 6*x^6 + 7*x^7 + 8*x^8 + 9*x^9) * A(x^10). - Ilya Gutkovskiy, Nov 14 2020
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EXAMPLE
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a(0) = 1 since an empty product is 1 by convention. a(120) = 1*2 = 2.
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MAPLE
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A051801 := proc(n) local d, j: d:=convert(n, base, 10): return mul(`if`(d[j]=0, 1, d[j]), j=1..nops(d)): end: seq(A051801(n), n=0..100); # Nathaniel Johnston, May 04 2011
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MATHEMATICA
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(Times@@Cases[IntegerDigits[#], Except[0]])&/@Range[0, 80] (* Harvey P. Dale, Jun 20 2011 *)
Table[Times@@(IntegerDigits[n]/.(0->1)), {n, 0, 80}] (* Harvey P. Dale, Apr 16 2023 *)
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PROG
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(Haskell)
a051801 0 = 1
a051801 n = (a051801 n') * (m + 0 ^ m) where (n', m) = divMod n 10
(Python)
from operator import mul
from functools import reduce
return reduce(mul, (int(d) for d in str(n) if d != '0')) if n > 0 else 1 # Chai Wah Wu, Aug 23 2014
(Python)
from math import prod
def a(n): return prod(int(d) for d in str(n) if d != '0')
(Swift 5)
A051801(n): String(n).compactMap{$0.wholeNumberValue == 0 ? 1 : $0.wholeNumberValue}.reduce(1, *) // Egor Khmara, Jan 15 2021
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CROSSREFS
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KEYWORD
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nonn,easy,base,nice
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AUTHOR
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STATUS
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approved
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