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

1,2

Comments

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

Links

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

Example

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.

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A346857 A332394 A220156 * A340868 A194454 A358398

Adjacent sequences: A333614 A333615 A333616 * A333618 A333619 A333620

Keyword

nonn,base

Author

Amiram Eldar, Mar 29 2020

Status

approved