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
Examples
a(0) = 1 since an empty product is 1 by convention. a(120) = 1*2 = 2.
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
Crossrefs
Programs
-
Haskell
a051801 0 = 1 a051801 n = (a051801 n') * (m + 0 ^ m) where (n',m) = divMod n 10 -- Reinhard Zumkeller, Nov 23 2011
-
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 *)
-
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
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
Comments