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

52022, 71824, 110201, 120472, 131072, 188180, 202312, 244634, 298374, 320305, 327184, 340000, 430000, 502150, 506056, 519168, 520220, 652118, 667815, 680000, 680625, 718240, 765625, 860000, 933156, 1001021, 1001047, 1003313, 1010113, 1035125, 1050232, 1215200

Offset: 1

Author

Amiram Eldar, Jan 07 2025

Keywords

• nonn
• base

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Pradip Kumar Pal and Kaushik Gopalan, Second Order Harshad Number, International Journal of Mathematical Education, Vol. 13, No. 1 (2023), pp. 25-26.

Crossrefs

Intersection of A065877 and A379980.

Equals A379980 \ A005349.

Programs

Mathematica

Select[Range[1.3*10^6], ! Divisible[#, Plus @@ IntegerDigits[#]] && Divisible[#, (Plus @@ (IntegerDigits[#]^2))^2] &]

PARI

isok(k) = k % sumdigits(k) && !(k % vecsum(apply(x->x^2, digits(k)))^2);

Python

def ok(n):
    d = list(map(int, str(n)))
    return n and n%sum(d) and n%sum(di**2 for di in d)**2 == 0
print([k for k in range(10**6) if ok(k)]) # Michael S. Branicky, Jan 10 2025

Formula

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.