cp's OEIS Frontend

A171671 Square numbers not of form m + sum of digits of m.

%I A171671 #28 Mar 26 2025 17:49:26
%S A171671 1,9,64,121,400,5776,6889,7396,8836,9409,10816,12100,17689,18769,
%T A171671 27556,29929,30976,33856,34969,37636,49729,65536,69169,69696,70756,
%U A171671 75076,75625,76729,80656,110224,124609,126736,132496,134689,156816,162409
%N A171671 Square numbers not of form m + sum of digits of m.
%C A171671 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.
%C A171671 Kaprekar (1963) introduced these numbers and called them self-square numbers. - _N. J. A. Sloane_, Oct 30 2014
%D A171671 D. R. Kaprekar, The Mathematics of the New Self Numbers, Privately Printed, 311 Devlali Camp, Devlali, India, 1963.
%H A171671 Amiram Eldar, <a href="/A171671/b171671.txt">Table of n, a(n) for n = 1..10000</a>
%H A171671 Shyam Sunder Gupta, <a href="https://doi.org/10.1007/978-981-97-2465-9_9">On Some Marvellous Numbers of Kaprekar</a>, Exploring the Beauty of Fascinating Numbers, Springer (2025) Ch. 9, 275-315.
%H A171671 D. R. Kaprekar, <a href="/A003052/a003052_2.pdf">The Mathematics of the New Self Numbers</a>. [annotated and scanned]
%H A171671 Zak Seidov, <a href="http://zak08.livejournal.com/17915.html">Self squares</a>.
%F A171671 a(n) = A171672(n)^2. - _Amiram Eldar_, Mar 26 2025
%t A171671 A062028=Table[n+Total[IntegerDigits[n]],{n,0,20000000}];
%t A171671 se=Select[Complement[Range[0,20000000],A062028],IntegerQ[Sqrt[ # ]]&]
%Y A171671 Intersection of A000290 and A003052 (self or Colombian numbers).
%Y A171671 Cf. A171672 (m^2 are self numbers), A062028 (a(n) = n + sum of the digits of n), A171673 (n and n^2 are self numbers), A382166.
%K A171671 base,nonn
%O A171671 1,2
%A A171671 _Zak Seidov_, Dec 15 2009
%E A171671 Changed the word "safe" in this entry to "self". - _N. J. A. Sloane_, Feb 26 2017