A360074 a(n) is the greatest divisor of n divisible by the sum of its own digits.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 12, 1, 7, 5, 8, 1, 18, 1, 20, 21, 2, 1, 24, 5, 2, 27, 7, 1, 30, 1, 8, 3, 2, 7, 36, 1, 2, 3, 40, 1, 42, 1, 4, 45, 2, 1, 48, 7, 50, 3, 4, 1, 54, 5, 8, 3, 2, 1, 60, 1, 2, 63, 8, 5, 6, 1, 4, 3, 70, 1, 72, 1, 2, 5, 4, 7, 6, 1, 80

Offset: 1

Author

Rémy Sigrist, Jan 24 2023

Keywords

• nonn
• base
• easy

Comments

Numbers divisible by the sum of their digits are called Niven (or Harshad, or harshad) numbers (A007602).

Examples

			For n = 32:
- the divisors of 32 are 1, 2, 4, 8, 16 and 32,
- 8 is divisible by 8 whereas 16 is not divisible by 1+6 and 32 is not divisible by 3+2,
- so a(32) = 8.
		

Links

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

Crossrefs

Cf. A005349, A332268, A360073.

Programs

Mathematica

Table[Max[Select[Divisors[n],Mod[#,Total[IntegerDigits[#]]]==0&]],{n,80}] (* Harvey P. Dale, Sep 04 2023 *)

PARI

a(n) = fordiv (n, d, my (t=n/d); if (t%sumdigits(t)==0, return (t)))

Formula

a(n) = n iff n belongs to A005349.