A333617 Numbers that are divisible by the sum of the digits of all their divisors (A034690).

1, 15, 52, 444, 495, 688, 810, 1782, 1891, 1950, 2028, 2058, 2295, 2970, 3007, 3312, 3510, 4092, 4284, 4681, 4687, 4824, 4992, 5143, 5307, 5356, 5487, 5742, 5775, 5829, 6724, 6750, 6900, 6913, 6972, 7141, 7471, 7560, 7650, 7722, 7783, 7807, 8280, 8325, 8700, 8721

Offset: 1

Author

Amiram Eldar, Mar 29 2020

Keywords

• nonn
• base

Comments

The corresponding quotients, k/A034690(k), are 1, 1, 2, 6, 5, 8, 6, 9, 61, ...

Examples

			15 is a term since its divisors are {1, 3, 5, 15}, and their sum of sums of digits is 1 + 3 + 5 + (1 + 5) = 15 which is a divisor of 15.
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A007953, A034690, A093705, A337230, A005349.

Programs

Mathematica

divDigSum[n_] := DivisorSum[n, Plus @@ IntegerDigits[#] &]; Select[Range[10^4], Divisible[#, divDigSum[#]] &]

PARI

isok(k) = k % sumdiv(k, d, sumdigits(d)) == 0; \\ Michel Marcus, Mar 30 2020

Python

from sympy import divisors
def sd(n): return sum(map(int, str(n)))
def ok(n): return n%sum(sd(d) for d in divisors(n)) == 0
def aupto(limit): return [m for m in range(1, limit+1) if ok(m)]
print(aupto(8721)) # Michael S. Branicky, Jan 15 2021