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

1,2

Links

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

Formula

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A003132, A034088, A169665, A169666.

Sequence in context: A269234 A160517 A072081 * A117562 A169663 A250602

Adjacent sequences: A034084 A034085 A034086 * A034088 A034089 A034090

Keyword

base,easy,nonn

Author

Erich Friedman

Status

approved