cp's OEIS Frontend

A379981 Non-Niven (or non-Harshad) numbers that are divisible by the square of the sum of the squares of their digits.

%I A379981 #16 Jan 11 2025 03:46:23
%S A379981 52022,71824,110201,120472,131072,188180,202312,244634,298374,320305,
%T A379981 327184,340000,430000,502150,506056,519168,520220,652118,667815,
%U A379981 680000,680625,718240,765625,860000,933156,1001021,1001047,1003313,1010113,1035125,1050232,1215200
%N A379981 Non-Niven (or non-Harshad) numbers that are divisible by the square of the sum of the squares of their digits.
%H A379981 Amiram Eldar, <a href="/A379981/b379981.txt">Table of n, a(n) for n = 1..10000</a>
%H A379981 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.
%F A379981 52022 is a term since 52022 is divisible by (5^2 + 2^2 + 0^2 + 2^2 + 2^2)^2 = 1369, but it is not divisible by 5 + 2 + 0 + 2 + 2 = 11.
%t A379981 Select[Range[1.3*10^6], ! Divisible[#, Plus @@ IntegerDigits[#]] && Divisible[#, (Plus @@ (IntegerDigits[#]^2))^2] &]
%o A379981 (PARI) isok(k) = k % sumdigits(k) && !(k % vecsum(apply(x->x^2, digits(k)))^2);
%o A379981 (Python)
%o A379981 def ok(n):
%o A379981     d = list(map(int, str(n)))
%o A379981     return n and n%sum(d) and n%sum(di**2 for di in d)**2 == 0
%o A379981 print([k for k in range(10**6) if ok(k)]) # _Michael S. Branicky_, Jan 10 2025
%Y A379981 Intersection of A065877 and A379980.
%Y A379981 Equals A379980 \ A005349.
%K A379981 nonn,base
%O A379981 1,1
%A A379981 _Amiram Eldar_, Jan 07 2025