# Generating necklaces by the FKM algorithm
# of Fredricksen, Kessler and Maiorana.
# See F. Ruskey, C. Savage, and T. M. Y. Wang,
# "Generating necklaces", Journal of Algorithms, 
# 13(3), 414 - 430, 1992.

# (SageMath)

def A054630_count(n, k):
    a = [0]*(n+1)
    #print "".join(map(str,a[1:]))
    count = 1; i = n
    if k == 1: return 1
    while true :
        a[i] += 1
        for j in (1..n-i): a[j+i] = a[j]
        if n % i == 0:
            count += 1
            #print "".join(map(str,a[1:]))
        i = n
        while a[i] == k-1: i -= 1
        if i == 0: break
    return count

for n in (1..6):
    print [A054630_count(k, n) for k in (1..n)]
	
# _Peter Luschny_, Aug 12 2012	

# (Julia)

function A054630Generate(n::Int, k::Int)
    necklace(a) = join(map(string, a[2:end]))
    a = fill(0, n+1)
    #println(necklace(a))
    count = 1; i = n
    k == 1 && return 1
    while i > 0
        a[i+1] += 1
        for j in 1:n-i a[j+i+1] = a[j+1] end
        if n % i == 0
            count += 1
            #println(necklace(a))
        end
        i = n
        while a[i+1] == k-1 i -= 1 end
    end
    return count
end

for n in 1:6
    println([A054630Generate(k, n) for k in 1:n])
end

# _Peter Luschny_, Sep 10 2018