cp's OEIS Frontend

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

%I A333617 #20 Jan 15 2021 15:55:44
%S A333617 1,15,52,444,495,688,810,1782,1891,1950,2028,2058,2295,2970,3007,3312,
%T A333617 3510,4092,4284,4681,4687,4824,4992,5143,5307,5356,5487,5742,5775,
%U A333617 5829,6724,6750,6900,6913,6972,7141,7471,7560,7650,7722,7783,7807,8280,8325,8700,8721
%N A333617 Numbers that are divisible by the sum of the digits of all their divisors (A034690).
%C A333617 The corresponding quotients, k/A034690(k), are 1, 1, 2, 6, 5, 8, 6, 9, 61, ...
%H A333617 David A. Corneth, <a href="/A333617/b333617.txt">Table of n, a(n) for n = 1..10000</a>
%e A333617 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.
%t A333617 divDigSum[n_] := DivisorSum[n, Plus @@ IntegerDigits[#] &]; Select[Range[10^4], Divisible[#, divDigSum[#]] &]
%o A333617 (PARI) isok(k) = k % sumdiv(k, d, sumdigits(d)) == 0; \\ _Michel Marcus_, Mar 30 2020
%o A333617 (Python)
%o A333617 from sympy import divisors
%o A333617 def sd(n): return sum(map(int, str(n)))
%o A333617 def ok(n): return n%sum(sd(d) for d in divisors(n)) == 0
%o A333617 def aupto(limit): return [m for m in range(1, limit+1) if ok(m)]
%o A333617 print(aupto(8721)) # _Michael S. Branicky_, Jan 15 2021
%Y A333617 Cf. A007953, A034690, A093705, A337230, A005349.
%K A333617 nonn,base
%O A333617 1,2
%A A333617 _Amiram Eldar_, Mar 29 2020