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

1,2

Comments

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

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Index entries for sequences related to divisors

Formula

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

Example

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.

Mathematica

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

Prog

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

Crossrefs

Cf. A005349, A332268, A360073.

Sequence in context: A203814 A373211 A346393 * A280505 A375968 A262401

Adjacent sequences: A360071 A360072 A360073 * A360075 A360076 A360077

Keyword

nonn,base,easy

Author

Rémy Sigrist, Jan 24 2023

Status

approved