A001102 Numbers k such that k / (sum of digits of k) is a square.

1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 24, 36, 48, 81, 100, 144, 150, 192, 200, 225, 288, 300, 320, 324, 375, 400, 441, 500, 512, 600, 640, 648, 700, 704, 735, 800, 832, 882, 900, 960, 1014, 1088, 1200, 1452, 1458, 1521, 1815, 2023

Offset: 1

Author

N. J. A. Sloane, Bill Moran (moran1(AT)llnl.gov)

Keywords

• nonn
• base
• nice

Comments

The sequence is infinite since if m = 10^(2*j) then m / digitsum(m) = m. - Marius A. Burtea, Dec 21 2018

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Subsequence of Niven numbers (A005349); cf. A028839.

Programs

Haskell

a001102 n = a001102_list !! (n-1)
a001102_list =
   filter (\x -> a010052 (x `div` (a007953 x)) == 1) a005349_list
-- Reinhard Zumkeller, Aug 17 2011

Magma

[n: n in [1..1000] | IsIntegral(n/(&+Intseq(n))) and IsSquare(n/(&+Intseq(n)))]; // Marius A. Burtea, Dec 21 2018

Mathematica

Select[Range[2200],IntegerQ[Sqrt[#/Total[IntegerDigits[#]]]]&] (* Harvey P. Dale, Feb 25 2012 *)

Formula

a(n) mod A007953(a(n)) = 0 and A010052(a(n) / A007953(a(n))) = 1. - Reinhard Zumkeller, Aug 17 2011