A352550 a(n) = number of modules with n elements over the ring of integers in the real quadratic field of discriminant 5.

1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 2, 0, 0, 2, 1, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 2, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 3, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2

Offset

1,11

Links

Table of n, a(n) for n=1..95.

Don Zagier, On the Number of n-Element Modules Over the Ring of Integers in a Quadratic Number Field [Based on email to N. J. A. Sloane, March 18 2022]

Prog

(PARI) \\ Don Zagier, Mar 18 2022
PZ(D, m=20) = Z=dirmul(vector(m, n, 1), vD=vector(m, n, kronecker(D, n))); v=Z; \
for(j=2, log(m)/log(2), V=v*0; for(k=1, m^(1/j), V[k^j]=Z[k]); v=dirmul(v, V)); v
PZ(5, 100)

Crossrefs

Cf. A038540, A038541, A248107, A352551-A352567.

Sequence in context: A339430 A375033 A350386 * A348326 A364213 A051907

Adjacent sequences: A352547 A352548 A352549 * A352551 A352552 A352553

Keyword

nonn

Author

N. J. A. Sloane, Mar 20 2022

Status

approved