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A054008 n read modulo (number of divisors of n).

%I A054008 #35 Oct 27 2023 22:00:45
%S A054008 0,0,1,1,1,2,1,0,0,2,1,0,1,2,3,1,1,0,1,2,1,2,1,0,1,2,3,4,1,6,1,2,1,2,
%T A054008 3,0,1,2,3,0,1,2,1,2,3,2,1,8,1,2,3,4,1,6,3,0,1,2,1,0,1,2,3,1,1,2,1,2,
%U A054008 1,6,1,0,1,2,3,4,1,6,1,0,1,2,1,0,1,2,3,0,1,6,3,2,1,2,3,0,1,2,3,1,1,6,1,0,1
%N A054008 n read modulo (number of divisors of n).
%C A054008 a(n)=0 iff n is a refactorable number (cf. A033950). - _Franz Vrabec_, Oct 16 2005
%C A054008 a(A066708(n)) = n and a(m) < n for m < A066708(n). - _Reinhard Zumkeller_, Sep 17 2014
%H A054008 Reinhard Zumkeller, <a href="/A054008/b054008.txt">Table of n, a(n) for n = 1..10000</a>
%F A054008 a(n) = n mod tau(n).
%p A054008 [ seq( i mod tau(i), i=1..130) ];
%t A054008 a[n_] := Mod[n, DivisorSigma[0, n]]; Array[a, 105] (* _Jean-François Alcover_, Sep 19 2017 *)
%o A054008 (Haskell)
%o A054008 a054008 n = n `mod` a000005 n  -- _Reinhard Zumkeller_, Sep 17 2014
%o A054008 (PARI) a(n) = n % numdiv(n); \\ _Michel Marcus_, Sep 19 2017
%o A054008 (Python)
%o A054008 from sympy import divisor_count
%o A054008 def A054008(n): return n%divisor_count(n) # _Chai Wah Wu_, Mar 14 2023
%Y A054008 Cf. A000005, A054009, A033950, A066708.
%K A054008 nonn
%O A054008 1,6
%A A054008 _Asher Auel_, Jan 12 2000