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A001102
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Numbers k such that k / (sum of digits of k) is a square.
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7
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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
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OFFSET
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1,2
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COMMENTS
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The sequence is infinite since if m = 10^(2*j) then m / digitsum(m) = m. - Marius A. Burtea, Dec 21 2018
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LINKS
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Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
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FORMULA
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a(n) mod A007953(a(n)) = 0 and A010052(a(n) / A007953(a(n))) = 1. - Reinhard Zumkeller, Aug 17 2011
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MATHEMATICA
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Select[Range[2200], IntegerQ[Sqrt[#/Total[IntegerDigits[#]]]]&] (* Harvey P. Dale, Feb 25 2012 *)
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PROG
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(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
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CROSSREFS
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Subsequence of Niven numbers (A005349); cf. A028839.
Sequence in context: A346535 A227224 A236750 * A051004 A032575 A038186
Adjacent sequences: A001099 A001100 A001101 * A001103 A001104 A001105
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KEYWORD
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nonn,base,nice
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AUTHOR
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N. J. A. Sloane, Bill Moran (moran1(AT)llnl.gov)
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STATUS
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approved
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