A362421 Number of nonisomorphic vector spaces consisting of n elements.

1, 1, 2, 1, 0, 1, 2, 2, 0, 1, 0, 1, 0, 0, 3, 1, 0, 1, 0, 0, 0, 1, 0, 2, 0, 2, 0, 1, 0, 1, 2, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 4, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 3, 0, 1, 0, 0, 0, 0, 0

Offset

2,3

Comments

If n is a prime power p^k, then a vector space consisting of n elements has the form (F_(p^d))^(k/d) where d is a divisor of k.

Links

Philip Turecek, Table of n, a(n) for n = 2..1000

Formula

a(n) = a(p^k) = sigma_0(k) if n = p^k is a prime power, a(n) = 0 otherwise.

Example

a(16) = 3 because 16=2^4 and 4 has 3 divisors.

Prog

(Sage)
def f(a):
    if not a.is_prime_power(): return 0
    else: return sigma(factor(a)[0][1], 0)

Crossrefs

Sequence in context: A177405 A379110 A378716 * A323302 A374212 A303903

Adjacent sequences: A362418 A362419 A362420 * A362422 A362423 A362424

Keyword

nonn

Author

Philip Turecek, Apr 19 2023

Status

approved