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

1, 10, 100, 1000, 1100, 1200, 1300, 2000, 2023, 2100, 2400, 3100, 4332, 5000, 10000, 10100, 10200, 10300, 11000, 12000, 13000, 20000, 20100, 20230, 20400, 21000, 24000, 30100, 30324, 31000, 31311, 42000, 43011, 43320, 50000, 52022, 52215, 55000, 71824, 100000

Offset

1,2

Comments

Called "Second-order Harshad numbers" by Pal and Gopalan (2023).

If k is a term, then 10*k is also a term.

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.

Example

10 is a term since 10 is divisible by (1^2 + 0^2)^2 = 1.
1100 is a term since 1100 is divisible by (1^2 + 1^2 + 0^2 + 0^2)^2 = 4.

Mathematica

Select[Range[10^5], Divisible[#, (Plus @@ (IntegerDigits[#]^2))^2] &]

Prog

(PARI) isok(k) = !(k % vecsum(apply(x -> x^2, digits(k)))^2);
(Python)
def ok(n): return n and n%sum(di**2 for di in map(int, str(n)))**2 == 0
print([k for k in range(100001) if ok(k)]) # Michael S. Branicky, Jan 10 2025

Crossrefs

Cf. A003132, A005349, A072081, A180490 (binary analog).

Subsequence of A034087.

Subsequences: A379981, A379982.

Sequence in context: A077439 A136839 A136863 * A031201 A228989 A072083

Adjacent sequences: A379977 A379978 A379979 * A379981 A379982 A379983

Keyword

nonn,base,easy

Author

Amiram Eldar, Jan 07 2025

Status

approved