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 A347042 #23 Nov 02 2024 09:14:17
%S A347042 0,1,1,2,1,3,1,2,2,3,1,3,1,3,3,3,1,3,1,3,3,3,1,5,2,3,2,3,1,4,1,2,3,3,
%T A347042 3,6,1,3,3,5,1,4,1,3,3,3,1,3,2,3,3,3,1,5,3,5,3,3,1,8,1,3,3,4,3,4,1,3,
%U A347042 3,4,1,3,1,3,3,3,3,4,1,3,3,3,1,8,3,3,3
%N A347042 Number of divisors d > 1 of n such that bigomega(d) divides bigomega(n), where bigomega = A001222.
%H A347042 Amiram Eldar, <a href="/A347042/b347042.txt">Table of n, a(n) for n = 1..10000</a>
%e A347042 The a(n) divisors for selected n:
%e A347042 n = 1: 2: 4: 6: 24: 30: 36: 60: 96: 144: 210: 216: 240: 360:
%e A347042 ---------------------------------------------------------------------
%e A347042 {} 2 2 2 2 2 2 2 2 2 2 2 2 2
%e A347042 4 3 3 3 3 3 3 3 3 3 3 3
%e A347042 6 4 5 4 4 4 4 5 4 4 4
%e A347042 6 30 6 5 6 6 6 6 5 5
%e A347042 24 9 6 8 8 7 8 6 6
%e A347042 36 10 12 9 10 9 8 8
%e A347042 15 96 12 14 12 10 9
%e A347042 60 18 15 18 12 10
%e A347042 144 21 27 15 12
%e A347042 35 216 20 15
%e A347042 210 30 18
%e A347042 240 20
%e A347042 30
%e A347042 45
%e A347042 360
%t A347042 Table[Length[Select[Rest[Divisors[n]],IntegerQ[PrimeOmega[n]/PrimeOmega[#]]&]],{n,100}]
%o A347042 (PARI) a(n) = my(bn=bigomega(n)); sumdiv(n, d, if (d>1, !(bn % bigomega(d)))); \\ _Michel Marcus_, Aug 18 2021
%o A347042 (Python)
%o A347042 from sympy import divisors, primeomega
%o A347042 def a(n):
%o A347042 bigomegan = primeomega(n)
%o A347042 return sum(bigomegan%primeomega(d) == 0 for d in divisors(n)[1:])
%o A347042 print([a(n) for n in range(1, 88)]) # _Michael S. Branicky_, Aug 18 2021
%o A347042 (Python)
%o A347042 from sympy import factorint, divisors
%o A347042 from sympy.utilities.iterables import multiset_combinations
%o A347042 def A347042(n):
%o A347042 fs = factorint(n,multiple=True)
%o A347042 return sum(len(list(multiset_combinations(fs,d))) for d in divisors(len(fs),generator=True)) # _Chai Wah Wu_, Aug 21 2021
%Y A347042 Positions of 1's are A000040.
%Y A347042 The smallest of these divisors is A020639
%Y A347042 The case of divisors with half bigomega is A345957 (rounded: A096825).
%Y A347042 A000005 counts divisors.
%Y A347042 A001221 counts distinct prime factors.
%Y A347042 A001222 counts all prime factors, also called bigomega.
%Y A347042 A056239 adds up prime indices, row sums of A112798.
%Y A347042 A207375 lists central divisors.
%Y A347042 Cf. A026424, A033676, A033677, A335433, A335448, A347045, A347046.
%K A347042 nonn
%O A347042 1,4
%A A347042 _Gus Wiseman_, Aug 17 2021