A034087 Numbers divisible by the sum of the squares of their digits.

1, 10, 20, 50, 100, 110, 111, 120, 130, 133, 200, 210, 240, 267, 298, 310, 315, 360, 372, 376, 400, 420, 480, 500, 532, 550, 630, 803, 917, 973, 1000, 1010, 1011, 1020, 1030, 1071, 1100, 1101, 1110, 1134, 1148, 1200, 1211, 1222, 1290, 1300, 1302, 1316

Offset: 1

Author

Erich Friedman

Keywords

• base
• easy
• nonn

Examples

			a(100) = 4131 since 4^2+1^2+3^2+1^2=27 divides 4131. - _Carmine Suriano_, May 04 2013
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..3465 from Carmine Suriano)

Crossrefs

Cf. A003132, A034088, A169665, A169666.

Programs

Maple

isA034087 := proc(n) if n mod A003132(n) = 0 then true ; else false ; end if ; end proc:
for n from 1 to 1800 do if isA034087(n) then printf("%d ",n) ; end if ; end do ; # R. J. Mathar, Feb 25 2007

Mathematica

Select[Range[1500], Divisible[#, Plus @@ (IntegerDigits[#]^2)] &] (* Amiram Eldar, Jan 31 2021 *)

PARI

isok(m) = !(m % norml2(digits(m))); \\ Michel Marcus, Jan 31 2021

Python

def ok(n): return n and n%sum(di**2 for di in map(int, str(n))) == 0
print([k for k in range(1317) if ok(k)]) # Michael S. Branicky, Jan 10 2025

Formula

A003132[a(n)] | a(n). - R. J. Mathar, Feb 25 2007