A072081 - OEIS

%I #35 Jan 10 2025 09:11:39

%S 1,10,20,50,81,100,112,162,200,243,324,392,400,405,500,512,605,648,

%T 810,972,1000,1053,1100,1120,1134,1183,1215,1296,1400,1620,1701,1900,

%U 1944,2000,2025,2106,2156,2240,2268,2300,2401,2430,2511,2592,2704,2800,2916

%N Numbers divisible by the square of the sum of their digits in base 10.

%C If k is a term, then 10 * k is a term. There are an infinite number of terms that are not divisible by 10. The numbers m = 24 * 10^(42 * k - 40) +1, k >= 1, are divisible by 7^2 = digsum(m)^2. Also, the numbers s = 491 * 10^(42 * k - 8) + 3, k >= 1, are divisible by 17^2 = digsum(s)^2. - _Marius A. Burtea_, Mar 19 2020

%C The numbers 2^A095412(n), n >= 5, are terms. - _Marius A. Burtea_, Apr 02 2020

%H Donovan Johnson, <a href="/A072081/b072081.txt">Table of n, a(n) for n = 1..1000</a>

%e k=9477, sumdigits(9477)=27, q=9477=27*27*13.

%t sud[x_] := Apply[Plus, IntegerDigits[x]] Do[s=sud[n]^2; If[IntegerQ[n/s], Print[n]], {n, 1, 10000}]

%t Select[Range[3000],Divisible[#,Total[IntegerDigits[#]]^2]&] (* _Harvey P. Dale_, May 04 2011 *)

%o (PARI) for(n=1,10^4,s=sumdigits(n);if(!(n%s^2),print1(n,", "))) \\ _Derek Orr_, Apr 29 2015

%o (Magma) [k:k in [1..3000]| k mod &+Intseq(k)^2 eq 0]; // _Marius A. Burtea_, Mar 19 2020

%o (Python)

%o def ok(n): return n and n%sum(di for di in map(int, str(n)))**2 == 0

%o print([k for k in range(3000) if ok(k)]) # _Michael S. Branicky_, Jan 10 2025

%Y Cf. A003132, A005349, A003634.

%K base,nonn,easy

%O 1,2

%A _Labos Elemer_, Jun 14 2002