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A063454
Number of solutions to x^3 + y^3 = z^3 mod n.
12
1, 4, 9, 20, 25, 36, 55, 112, 189, 100, 121, 180, 109, 220, 225, 448, 289, 756, 487, 500, 495, 484, 529, 1008, 725, 436, 2187, 1100, 841, 900, 1081, 2048, 1089, 1156, 1375, 3780, 973, 1948, 981, 2800, 1681, 1980, 1513, 2420, 4725, 2116, 2209, 4032
OFFSET
1,2
COMMENTS
Equivalently, the number of solutions to x^3 + y^3 + z^3 == 0 (mod n). - Andrew Howroyd, Jul 18 2018
LINKS
Chai Wah Wu, Table of n, a(n) for n = 1..10000 (terms n = 1..1000 from Seiichi Manyama)
PROG
(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
(Python)
def A063454(n):
ndict = {}
for i in range(n):
m = pow(i, 3, n)
if m in ndict:
ndict[m] += 1
else:
ndict[m] = 1
count = 0
for i in ndict:
ni = ndict[i]
for j in ndict:
k = (i+j) % n
if k in ndict:
count += ni*ndict[j]*ndict[k]
return count # Chai Wah Wu, Jun 06 2017
CROSSREFS
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).
Sequence in context: A115075 A288102 A288100 * A288104 A053807 A327238
KEYWORD
nonn,mult
AUTHOR
Ahmed Fares (ahmedfares(AT)my-deja.com), Jul 25 2001
EXTENSIONS
More terms from Dean Hickerson, Jul 26, 2001
STATUS
approved