cp's OEIS Frontend

A379980 Numbers that are divisible by the square of the sum of the squares of their digits.

%I A379980 #21 Jan 11 2025 03:45:49
%S A379980 1,10,100,1000,1100,1200,1300,2000,2023,2100,2400,3100,4332,5000,
%T A379980 10000,10100,10200,10300,11000,12000,13000,20000,20100,20230,20400,
%U A379980 21000,24000,30100,30324,31000,31311,42000,43011,43320,50000,52022,52215,55000,71824,100000
%N A379980 Numbers that are divisible by the square of the sum of the squares of their digits.
%C A379980 Called "Second-order Harshad numbers" by Pal and Gopalan (2023).
%C A379980 If k is a term, then 10*k is also a term.
%H A379980 Amiram Eldar, <a href="/A379980/b379980.txt">Table of n, a(n) for n = 1..10000</a>
%H A379980 Pradip Kumar Pal and Kaushik Gopalan, <a href="https://www.ripublication.com/ijome23/ijomev13n1_04.pdf">Second Order Harshad Number</a>, International Journal of Mathematical Education, Vol. 13, No. 1 (2023), pp. 25-26.
%e A379980 10 is a term since 10 is divisible by (1^2 + 0^2)^2 = 1.
%e A379980 1100 is a term since 1100 is divisible by (1^2 + 1^2 + 0^2 + 0^2)^2 = 4.
%t A379980 Select[Range[10^5], Divisible[#, (Plus @@ (IntegerDigits[#]^2))^2] &]
%o A379980 (PARI) isok(k) = !(k % vecsum(apply(x -> x^2, digits(k)))^2);
%o A379980 (Python)
%o A379980 def ok(n): return n and n%sum(di**2 for di in map(int, str(n)))**2 == 0
%o A379980 print([k for k in range(100001) if ok(k)]) # _Michael S. Branicky_, Jan 10 2025
%Y A379980 Cf. A003132, A005349, A072081, A180490 (binary analog).
%Y A379980 Subsequence of A034087.
%Y A379980 Subsequences: A379981, A379982.
%K A379980 nonn,base,easy
%O A379980 1,2
%A A379980 _Amiram Eldar_, Jan 07 2025