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A171671
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Square numbers not of form n + sum of digits of n.
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3
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1, 9, 64, 121, 400, 5776, 6889, 7396, 8836, 9409, 10816, 12100, 17689, 18769, 27556, 29929, 30976, 33856, 34969, 37636, 49729, 65536, 69169, 69696, 70756, 75076, 75625, 76729, 80656, 110224, 124609, 126736, 132496, 134689, 156816, 162409
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OFFSET
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1,2
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COMMENTS
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We may call these numbers the self or Colombian squares. Subsequence of A003052. There are 446 such self squares < 2*10^7, 218 odd and 228 even.
Kaprekar (1963) introduced these numbers and called them self-square numbers. - N. J. A. Sloane, Oct 30 2014
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REFERENCES
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D. R. Kaprekar, The Mathematics of the New Self Numbers, Privately Printed, 311 Devlali Camp, Devlali, India, 1963.
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LINKS
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MATHEMATICA
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A062028=Table[n+Total[IntegerDigits[n]], {n, 0, 20000000}];
se=Select[Complement[Range[0, 20000000], A062028], IntegerQ[Sqrt[ # ]]&]
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CROSSREFS
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Cf. A003052 (Self or Colombian numbers), A171672 (n^2 are self numbers), A062028 (a(n) = n + sum of the digits of n), A171673 (n and n^2 are self numbers).
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KEYWORD
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base,nonn
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AUTHOR
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EXTENSIONS
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Changed the word "safe" in this entry to "self". - N. J. A. Sloane, Feb 26 2017
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STATUS
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approved
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