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

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

Adjacent sequences: A063451 A063452 A063453 * A063455 A063456 A063457

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