This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A345957 #20 Aug 21 2021 13:22:04
%S A345957 1,0,0,1,0,2,0,0,1,2,0,0,0,2,2,1,0,0,0,0,2,2,0,2,1,2,0,0,0,0,0,0,2,2,
%T A345957 2,3,0,2,2,2,0,0,0,0,0,2,0,0,1,0,2,0,0,2,2,2,2,2,0,4,0,2,0,1,2,0,0,0,
%U A345957 2,0,0,0,0,2,0,0,2,0,0,0,1,2,0,4,2,2,2
%N A345957 Number of divisors of n with exactly half as many prime factors as n, counting multiplicity.
%C A345957 These divisors do not necessarily include the central divisors (A207375), and may not themselves be central.
%e A345957 The a(n) divisors for selected n:
%e A345957 n = 1: 6: 36: 60: 210: 840: 900: 1260: 1296: 3600:
%e A345957 --------------------------------------------------------
%e A345957 1 2 4 4 6 8 12 12 16 16
%e A345957 3 6 6 10 12 18 18 24 24
%e A345957 9 10 14 20 20 20 36 36
%e A345957 15 15 28 30 28 54 40
%e A345957 21 30 45 30 81 60
%e A345957 35 42 50 42 90
%e A345957 70 75 45 100
%e A345957 105 63 150
%e A345957 70 225
%e A345957 105
%t A345957 Table[Length[Select[Divisors[n],PrimeOmega[#]==PrimeOmega[n]/2&]],{n,100}]
%o A345957 (PARI) a(n) = my(nb=bigomega(n)); sumdiv(n, d, 2*bigomega(d) == nb); \\ _Michel Marcus_, Aug 16 2021
%o A345957 (Python)
%o A345957 from sympy import divisors, factorint
%o A345957 def a(n):
%o A345957 npf = len(factorint(n, multiple=True))
%o A345957 divs = divisors(n)
%o A345957 return sum(2*len(factorint(d, multiple=True)) == npf for d in divs)
%o A345957 print([a(n) for n in range(1, 88)]) # _Michael S. Branicky_, Aug 17 2021
%o A345957 (Python 3.8+)
%o A345957 from itertools import combinations
%o A345957 from math import prod, comb
%o A345957 from sympy import factorint
%o A345957 def A345957(n):
%o A345957 if n == 1:
%o A345957 return 1
%o A345957 fs = factorint(n)
%o A345957 elist = list(fs.values())
%o A345957 q, r = divmod(sum(elist),2)
%o A345957 k = len(elist)
%o A345957 if r:
%o A345957 return 0
%o A345957 c = 0
%o A345957 for i in range(k+1):
%o A345957 m = (-1)**i
%o A345957 for d in combinations(range(k),i):
%o A345957 t = k+q-sum(elist[j] for j in d)-i-1
%o A345957 if t >= 0:
%o A345957 c += m*comb(t,k-1)
%o A345957 return c # _Chai Wah Wu_, Aug 20 2021
%o A345957 (Python)
%o A345957 from sympy import factorint
%o A345957 from sympy.utilities.iterables import multiset_combinations
%o A345957 def A345957(n):
%o A345957 if n == 1:
%o A345957 return 1
%o A345957 fs = factorint(n,multiple=True)
%o A345957 q, r = divmod(len(fs),2)
%o A345957 return 0 if r else len(list(multiset_combinations(fs,q))) # _Chai Wah Wu_, Aug 20 2021
%Y A345957 The case of powers of 2 is A000035.
%Y A345957 Positions of even terms are A000037.
%Y A345957 Positions of odd terms are A000290.
%Y A345957 Positions of 0's are A026424.
%Y A345957 Positions of 1's are A056798.
%Y A345957 The rounded version is A096825.
%Y A345957 The case of all divisors (not just 2) is A347042.
%Y A345957 The smallest of these divisors is A347045 (rounded: A347043).
%Y A345957 The greatest of these divisors is A347046 (rounded: A347044).
%Y A345957 A000005 counts divisors.
%Y A345957 A001221 counts distinct prime factors.
%Y A345957 A001222 counts all prime factors.
%Y A345957 A056239 adds up prime indices, row sums of A112798.
%Y A345957 A207375 lists central divisors.
%Y A345957 A325534 counts separable partitions, ranked by A335433.
%Y A345957 A325535 counts inseparable partitions, ranked by A335448.
%Y A345957 A334997 counts chains of divisors of n by length.
%Y A345957 Cf. A001227, A001414, A028260, A033676, A033677, A073093, A074206, A217581, A344653, A346697-A346704.
%K A345957 nonn
%O A345957 1,6
%A A345957 _Gus Wiseman_, Aug 16 2021