A360073 a(n) is the greatest divisor of n divisible by the product of its own digits.

1, 2, 3, 4, 5, 6, 7, 8, 9, 5, 11, 12, 1, 7, 15, 8, 1, 9, 1, 5, 7, 11, 1, 24, 5, 2, 9, 7, 1, 15, 1, 8, 11, 2, 7, 36, 1, 2, 3, 8, 1, 7, 1, 11, 15, 2, 1, 24, 7, 5, 3, 4, 1, 9, 11, 8, 3, 2, 1, 15, 1, 2, 9, 8, 5, 11, 1, 4, 3, 7, 1, 36, 1, 2, 15, 4, 11, 6, 1, 8, 9

Offset: 1

Author

Rémy Sigrist, Jan 24 2023

Keywords

• nonn
• base
• easy

Comments

Numbers divisible by the product of their digits are called Zuckerman numbers (A007602).

Examples

			For n = 10:
- the divisors of 10 are 1, 2, 5 and 10,
- 5 is divisible by 5 whereas 10 is not divisible by 1*0,
- so a(10) = 5.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to divisors

Crossrefs

Cf. A007602, A335037, A337941, A360074.

Programs

PARI

a(n) = { fordiv (n, d, my (t=n/d, p=vecprod(digits(t))); if (p && t%p==0, return (t))) }

Formula

a(n) = n iff n belongs to A007602.