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A063454 Number of solutions to x^3 + y^3 = z^3 mod n.

%I A063454 #22 Jul 02 2025 20:00:45
%S A063454 1,4,9,20,25,36,55,112,189,100,121,180,109,220,225,448,289,756,487,
%T A063454 500,495,484,529,1008,725,436,2187,1100,841,900,1081,2048,1089,1156,
%U A063454 1375,3780,973,1948,981,2800,1681,1980,1513,2420,4725,2116,2209,4032
%N A063454 Number of solutions to x^3 + y^3 = z^3 mod n.
%C A063454 Equivalently, the number of solutions to x^3 + y^3 + z^3 == 0 (mod n). - _Andrew Howroyd_, Jul 18 2018
%H A063454 Chai Wah Wu, <a href="/A063454/b063454.txt">Table of n, a(n) for n = 1..10000</a> (terms n = 1..1000 from Seiichi Manyama)
%o A063454 (PARI) a(n)={my(p=Mod(sum(i=0, n-1, x^(i^3%n)), 1-x^n)); polcoeff(lift(p^3), 0)} \\ _Andrew Howroyd_, Jul 18 2018
%o A063454 (Python)
%o A063454 def A063454(n):
%o A063454     ndict = {}
%o A063454     for i in range(n):
%o A063454         m = pow(i,3,n)
%o A063454         if m in ndict:
%o A063454             ndict[m] += 1
%o A063454         else:
%o A063454             ndict[m] = 1
%o A063454     count = 0
%o A063454     for i in ndict:
%o A063454         ni = ndict[i]
%o A063454         for j in ndict:
%o A063454             k = (i+j) % n
%o A063454             if k in ndict:
%o A063454                 count += ni*ndict[j]*ndict[k]
%o A063454     return count # _Chai Wah Wu_, Jun 06 2017
%Y A063454 Number of solutions to x^k + y^k = z^k mod n: A062775 (k=2), this sequence (k=3), A288099 (k=4), A288100 (k=5), A288101 (k=6), A288102 (k=7), A288103 (k=8), A288104 (k=9), A288105 (k=10).
%K A063454 nonn,mult
%O A063454 1,2
%A A063454 Ahmed Fares (ahmedfares(AT)my-deja.com), Jul 25 2001
%E A063454 More terms from _Dean Hickerson_, Jul 26 2001