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A051801 Product of the nonzero digits of n. 41
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
Zak Seidov and Michael De Vlieger, Table of n, a(n) for n = 0..10000 (First 1000 terms from Zak Seidov)
FORMULA
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
a(n) = A007954(A004719(n)). - Michel Marcus, Mar 07 2022
EXAMPLE
a(0) = 1 since an empty product is 1 by convention. a(120) = 1*2 = 2.
MAPLE
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
MATHEMATICA
(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 *)
PROG
(Haskell)
a051801 0 = 1
a051801 n = (a051801 n') * (m + 0 ^ m) where (n', m) = divMod n 10
-- Reinhard Zumkeller, Nov 23 2011
(PARI) a(n)=my(v=select(k->k>1, digits(n))); prod(i=1, #v, v[i]) \\ Charles R Greathouse IV, Nov 20 2012
(Python)
from operator import mul
from functools import reduce
def A051801(n):
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')
print([a(n) for n in range(74)]) # Michael S. Branicky, Jul 18 2021
(Swift 5)
A051801(n): String(n).compactMap{$0.wholeNumberValue == 0 ? 1 : $0.wholeNumberValue}.reduce(1, *) // Egor Khmara, Jan 15 2021
CROSSREFS
Basis for A051802.
See A338882 for similar sequences.
See also A007953 (digital sum).
Sequence in context: A067456 A052429 A051802 * A071205 A066750 A217928
KEYWORD
nonn,easy,base,nice
AUTHOR
Dan Hoey, Dec 09 1999
STATUS
approved

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Last modified June 5 21:20 EDT 2023. Contains 363138 sequences. (Running on oeis4.)