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

1,1

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.

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.

Mathematica

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

Prog

(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

Crossrefs

Intersection of A065877 and A379980.

Equals A379980 \ A005349.

Sequence in context: A234181 A031679 A234679 * A191303 A291869 A186849

Adjacent sequences: A379978 A379979 A379980 * A379982 A379983 A379984

Keyword

nonn,base

Author

Amiram Eldar, Jan 07 2025

Status

approved