login
A171671
Square numbers not of form n + sum of digits of n.
3
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
OFFSET
1,2
COMMENTS
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
REFERENCES
D. R. Kaprekar, The Mathematics of the New Self Numbers, Privately Printed, 311 Devlali Camp, Devlali, India, 1963.
LINKS
D. R. Kaprekar, The Mathematics of the New Self Numbers [annotated and scanned]
Zak Seidov, Safe squares
MATHEMATICA
A062028=Table[n+Total[IntegerDigits[n]], {n, 0, 20000000}];
se=Select[Complement[Range[0, 20000000], A062028], IntegerQ[Sqrt[ # ]]&]
CROSSREFS
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).
Sequence in context: A302975 A165447 A050792 * A016886 A099761 A018201
KEYWORD
base,nonn
AUTHOR
Zak Seidov, Dec 15 2009
EXTENSIONS
Changed the word "safe" in this entry to "self". - N. J. A. Sloane, Feb 26 2017
STATUS
approved