A061910 Positive numbers k such that sum of digits of k^2 is a square.
1, 2, 3, 6, 9, 10, 11, 12, 13, 14, 15, 18, 20, 21, 22, 23, 30, 31, 39, 41, 45, 48, 51, 58, 59, 60, 67, 68, 76, 77, 85, 86, 90, 94, 95, 100, 101, 102, 103, 104, 105, 110, 111, 112, 113, 120, 121, 122, 130, 131, 139, 140, 148, 150, 157, 158, 166, 175, 176, 180, 184, 185
Offset: 1
Examples
6^2 = 36 and 3+6 = 9 is a square. 13^2 = 169 and 1+6+9 = 16 is a square.
Links
- Bruno Berselli, Table of n, a(n) for n = 1..1000
- MathStackExchange, Numbers n such that the digit sum of n2 is a square, 2015-2016.
Crossrefs
Programs
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Magma
[ n: n in [1..185] | IsSquare(&+Intseq(n^2)) ]; // Bruno Berselli, Jul 29 2011
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Maple
readlib(issqr): f := []: for n from 1 to 200 do if issqr(convert(convert(n^2,base,10),`+`)) then f := [op(f), n] fi; od; f;
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Mathematica
Select[Range[185], IntegerQ[Sqrt[Total[IntegerDigits[#^2]]]] &] (* Jayanta Basu, May 06 2013 *)
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PARI
is(n)=n=eval(Vec(Str(n^2)));issquare(sum(i=1,#n,n[i])) \\ Charles R Greathouse IV, Jul 29 2011
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PARI
select( is_A061910(n)=issquare(sumdigits(n^2)), [0..199]) \\ Includes the initial 0. - M. F. Hasler, Oct 16 2017
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Python
from gmpy2 import is_square A061910 = [n for n in range(1,10**3) if is_square(sum(int(d) for d in str(n*n)))] # Chai Wah Wu, Sep 03 2014