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A087786 a(n) = number of solutions to x^3 - y^3 == 0 (mod n). 6

%I

%S 1,2,3,6,5,6,19,20,27,10,11,18,37,38,15,40,17,54,55,30,57,22,23,60,45,

%T 74,135,114,29,30,91,112,33,34,95,162,109,110,111,100,41,114,127,66,

%U 135,46,47,120,175,90,51,222,53,270,55,380,165,58,59,90,181,182,513,352,185

%N a(n) = number of solutions to x^3 - y^3 == 0 (mod n).

%H Andrew Howroyd, <a href="/A087786/b087786.txt">Table of n, a(n) for n = 1..10000</a>

%F Multiplicative with a(p^e) = p^(2*floor(2*e/3)) + Sum_{i=0..floor((e-1)/3)} k*(p-1)*p^(e+i-1) where k = 3 if (p = 3 and 3*i+1 = e) or (p mod 3 = 1) otherwise k = 1. - _Andrew Howroyd_, Jul 17 2018

%o (PARI) a(n)={my(v=vector(n)); for(i=0, n-1, v[i^3%n + 1]++); sum(i=0, n-1, v[i+1]^2)} \\ _Andrew Howroyd_, Jul 17 2018

%o (PARI) a(n)={my(f=factor(n)); prod(i=1, #f~, my(p=f[i,1], e=f[i,2]); p^(2*(2*e\3)) + sum(i=0, (e-1)\3, if(p%3==1 || (p==3&&3*i<e-1), 3, 1)*(p-1)*p^(e+i-1)) )} \\ _Andrew Howroyd_, Jul 17 2018

%Y Cf. A046530, A087694, A062803.

%K mult,nonn

%O 1,2

%A Yuval Dekel (dekelyuval(AT)hotmail.com), Oct 06 2003

%E More terms from _John W. Layman_, Oct 18 2003

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Last modified August 9 02:14 EDT 2020. Contains 336310 sequences. (Running on oeis4.)