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Numbers n such that n*n/k is an integer. n=(x_1 x_2 ... x_r) where x_i are digits of n, k = x_1^2 + x_2^2 + ... + x_r^2.
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%I #17 Aug 13 2015 04:36:18

%S 1,2,3,4,5,6,7,8,9,10,20,30,40,50,60,70,80,90,100,110,111,114,120,130,

%T 133,170,200,210,220,222,228,240,260,266,267,298,300,310,315,330,333,

%U 340,360,372,376,390,399,400,420,430,440,444,480,500,532,550,555,600

%N Numbers n such that n*n/k is an integer. n=(x_1 x_2 ... x_r) where x_i are digits of n, k = x_1^2 + x_2^2 + ... + x_r^2.

%H Ivan Neretin, <a href="/A180480/b180480.txt">Table of n, a(n) for n = 1..10000</a>

%e n=267, 267*267/(2*2+6*6+7*7)=801, n=267 belongs to the sequence.

%p filter:= proc(n)

%p type(n^2/convert(map(`^`,convert(n,base,10),2),`+`),integer)

%p end proc:

%p select(filter, [$1..1000]); # _Robert Israel_, Aug 03 2015

%t Select[Range[600], Divisible[#^2, Plus @@ (IntegerDigits[#]^2)] &] (* _Ivan Neretin_, Aug 03 2015 *)

%o (PARI) k(n)=apply(sqr,digits(n));

%o is_ok(n)=my(kk=vecsum(k(n)));n*n\kk===n*n/kk;

%o first(m)=my(v=vector(m),k=1);for(i=1,m,while(!is_ok(k),k++);v[i]=k;k++);v; \\ _Anders Hellström_, Aug 03 2015

%Y Cf. A005349

%K base,easy,nonn

%O 1,2

%A _Ctibor O. Zizka_, Sep 07 2010