A051801 Product of the nonzero digits of n.

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

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)

Index entries for Colombian or self numbers and related sequences

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) // 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).

Cf. A004719, A007954.

Sequence in context: A067456 A052429 A051802 * A071205 A066750 A371383

Adjacent sequences: A051798 A051799 A051800 * A051802 A051803 A051804

Keyword

nonn,easy,base,nice

Author

Dan Hoey, Dec 09 1999

Status

approved