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A236750
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Positive integers k such that k^3 divided by the digital sum of k is a square.
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4
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1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 24, 36, 48, 81, 100, 144, 150, 192, 196, 200, 225, 242, 288, 300, 320, 324, 375, 400, 441, 484, 500, 512, 600, 640, 648, 700, 704, 735, 800, 832, 882, 900, 960, 1014, 1088, 1200, 1250, 1452, 1458, 1521, 1815, 2023, 2025, 2028
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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^3 / digitsum(m) = m^(6*k). - Marius A. Burtea, Dec 21 2018
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LINKS
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EXAMPLE
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192 is in the sequence because the digital sum of 192 is 12, and 192^3/12 = 589824 = 768^2.
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PROG
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(PARI)
s=[]; for(n=1, 5000, d=sumdigits(n); if(n^3%d==0 && issquare(n^3\d), s=concat(s, n))); s
(Magma) [n: n in [1..1500] | IsIntegral((n^3)/(&+Intseq(n))) and IsSquare((n^3)/(&+Intseq(n)))]; // Marius A. Burtea, Dec 21 2018
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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