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A333617 Numbers that are divisible by the sum of the digits of all their divisors (A034690). 7
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 (list; graph; refs; listen; history; text; internal format)
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 A219384

Adjacent sequences:  A333614 A333615 A333616 * A333618 A333619 A333620

KEYWORD

nonn,base

AUTHOR

Amiram Eldar, Mar 29 2020

STATUS

approved

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Last modified September 27 04:10 EDT 2021. Contains 347673 sequences. (Running on oeis4.)