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A185027 Sum of the triangular divisors of n. 6

%I

%S 1,1,4,1,1,10,1,1,4,11,1,10,1,1,19,1,1,10,1,11,25,1,1,10,1,1,4,29,1,

%T 35,1,1,4,1,1,46,1,1,4,11,1,31,1,1,64,1,1,10,1,11,4,1,1,10,56,29,4,1,

%U 1,35,1,1,25,1,1,76,1,1,4,11,1,46,1,1,19,1,1,88,1

%N Sum of the triangular divisors of n.

%H Antonio Roldán, <a href="/A185027/b185027.txt">Table of n, a(n) for n = 1..10000</a>

%F G.f.: Sum_{k>=1} (k*(k + 1)/2)*x^(k*(k+1)/2)/(1 - x^(k*(k+1)/2)). - _Ilya Gutkovskiy_, Dec 24 2016

%e a(15) = 19 because 1+3+15 = 19 (1, 3 and 15 triangular divisors of 15).

%o (PARI)

%o istriang(x)=issquare(8*x+1)

%o sumdivtriang(n)=m=0;for(i=1,n,if(istriang(i)&&n/i==n\i,m+=i));return(m)}

%o {for(n=1,10^4,k=sumdivtriang(n);write("b185027.txt",n," ",k))}

%o (PARI) a(n)=sumdiv(n, d, ispolygonal(d, 3)*d) \\ _Charles R Greathouse IV_, Jan 14 2013

%Y Cf. A035316.

%K nonn

%O 1,3

%A _Antonio Roldán_, Jan 14 2013

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Last modified January 20 11:11 EST 2020. Contains 331083 sequences. (Running on oeis4.)