A379982 Nonmultiples of 10 that are divisible by the square of the sum of the squares of their digits.

1, 2023, 4332, 30324, 31311, 43011, 52022, 52215, 71824, 101376, 110201, 116964, 120213, 120472, 120612, 131072, 141312, 145152, 202312, 230202, 233928, 244634, 298374, 305252, 320305, 327184, 409374, 506056, 511104, 519168, 565152, 615627, 652118, 667815, 680625

Offset: 1

Author

Amiram Eldar, Jan 07 2025

Keywords

• nonn
• base

Examples

			2023 is a term since 2023 is not divisible by 10 and it is divisible by (2^2 + 0^2 + 2^2 + 3^2)^2 = 289.
		

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 A067251 and A379980.

Programs

Mathematica

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

PARI

isok(k) = k % 10 && !(k % vecsum(apply(x -> x^2, digits(k)))^2);

Python

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