cp's OEIS Frontend

A236748 Positive integers k such that k^2 divided by the digital sum of k is a square.

%I A236748 #38 Sep 08 2022 08:46:06
%S A236748 1,4,9,10,18,22,27,36,40,45,54,63,72,81,88,90,100,108,112,117,126,130,
%T A236748 135,144,153,162,171,180,196,202,207,216,220,225,234,243,252,261,268,
%U A236748 270,306,310,315,324,333,342,351,360,376,400,405,414,423,432,441
%N A236748 Positive integers k such that k^2 divided by the digital sum of k is a square.
%C A236748 Subsequence of A028839 (sum of digits of n is a square). - _Jon Perry_ and _Michel Marcus_, Oct 30 2014
%C A236748 A028839 is the sequence of positive integers such that n^2 divided by the sum of the digits is a rational square. For this sequence, it is required to be an integer square. - _Franklin T. Adams-Watters_, Oct 30 2014
%C A236748 The sequence is infinite since if m = 10^j then m^2 / digitsum(m) = m^2. - _Marius A. Burtea_, Dec 21 2018
%H A236748 Colin Barker, <a href="/A236748/b236748.txt">Table of n, a(n) for n = 1..1000</a>
%e A236748 153 is in the sequence because the digital sum of 153 is 9, and 153^2/9 = 2601 = 51^2.
%p A236748 filter:= n -> issqr(n^2/convert(convert(n,base,10),`+`)):
%p A236748 select(filter, [$1..10000]); # _Robert Israel_, Oct 30 2014
%t A236748 Select[Range[500],IntegerQ[Sqrt[#^2/Total[IntegerDigits[#]]]]&] (* _Harvey P. Dale_, Nov 19 2014 *)
%o A236748 (PARI) s=[]; for(n=1, 600, d=sumdigits(n); if(n^2%d==0 && issquare(n^2\d), s=concat(s, n))); s
%o A236748 (Magma) [n: n in [1..1500] | IsIntegral((n^2)/(&+Intseq(n))) and IsSquare((n^2)/(&+Intseq(n)))]; // _Marius A. Burtea_, Dec 21 2018
%Y A236748 Cf. A001102, A007953, A236749, A236750, A236751.
%Y A236748 Cf. A028839.
%K A236748 nonn,base
%O A236748 1,2
%A A236748 _Colin Barker_, Jan 30 2014