A236652 - OEIS

%I #11 Jun 13 2015 00:54:57

%S 1,4,9,10,18,19,22,27,28,36,37,40,45,46,54,55,58,63,64,72,73,76,81,82,

%T 90,91,94,99,100,108,109,112,117,118,126,127,130,135,136,144,145,148,

%U 153,154,162,163,166,171,172,180,181,184,189,190,198,199,202,207

%N Positive integers n such that n^2 divided by the digital root of n is a square.

%H Colin Barker, <a href="/A236652/b236652.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,1,-1).

%F a(n) = a(n-1)+a(n-5)-a(n-6).

%F G.f.: x*(8*x^4+x^3+5*x^2+3*x+1) / ((x-1)^2*(x^4+x^3+x^2+x+1)).

%e 18 is in the sequence because the digital root of 18 is 9, and 18^2/9 = 36 = 6^2.

%o (PARI) s=[]; for(n=1, 300, d=(n-1)%9+1; if(n^2%d==0 && issquare(n^2\d), s=concat(s, n))); s

%o (PARI) Vec(x*(8*x^4+x^3+5*x^2+3*x+1)/((x-1)^2*(x^4+x^3+x^2+x+1)) + O(x^100))

%Y Cf. A010888, A236653.

%K nonn,base,easy

%O 1,2

%A _Colin Barker_, Jan 29 2014