A063543 a(n) = n - product of the nonzero digits of n.

0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 18, 19, 18, 17, 16, 15, 14, 13, 12, 11, 27, 28, 26, 24, 22, 20, 18, 16, 14, 12, 36, 37, 34, 31, 28, 25, 22, 19, 16, 13, 45, 46, 42, 38, 34, 30, 26, 22, 18, 14, 54, 55, 50, 45, 40, 35, 30, 25, 20, 15, 63, 64, 58

Offset: 1

Author

N. J. A. Sloane, Aug 14 2001

Keywords

• nonn
• base
• easy
• look

Comments

The graph somewhat resembles wisteria flowers.

Examples

			a(20) = 20 - 2 = 18.
		

Links

• Harry J. Smith, Table of n, a(n) for n = 1..2000
• N. J. A. Sloane and Brady Haran, Amazing Graphs II (including Star Wars), Numberphile video (2019).

Crossrefs

Cf. A051801, A063114.

Programs

Magma

[n - &*[a: k in [1..#Intseq(n)] | a ne 0 where a is Intseq(n)[k]]: n in [1..100]]; // Marius A. Burtea, Sep 16 2019

Maple

a:= n-> n-mul(i, i=subs(0=1, convert(n, base, 10))):
seq(a(n), n=1..80);  # Alois P. Heinz, Aug 18 2019

Mathematica

Table[n - Times@@DeleteCases[IntegerDigits[n], 0], {n, 70}] (* Alonso del Arte, Dec 15 2013 *)

PARI

a(n) = my(d=select(x->(x!=0), digits(n))); n - vecprod(d); \\ Michel Marcus, Jan 13 2020

Python

def a(n):
    digits = map(int, str(n))
    product = 1
    for d in digits:
        if d != 0:
            product *= d
    return n - product
[a(n) for n in range(20)]
# Elisabeth Zemack, Sep 16 2019; corrected by Fabio Somenzi, Jan 13 2020

Formula

a(n) = n - A051801(n).

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Aug 14 2001