A054008 - OEIS

%I #35 Oct 27 2023 22:00:45

%S 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 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 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 n read modulo (number of divisors of n).

%C a(n)=0 iff n is a refactorable number (cf. A033950). - _Franz Vrabec_, Oct 16 2005

%C a(A066708(n)) = n and a(m) < n for m < A066708(n). - _Reinhard Zumkeller_, Sep 17 2014

%H Reinhard Zumkeller, <a href="/A054008/b054008.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = n mod tau(n).

%p [ seq( i mod tau(i), i=1..130) ];

%t a[n_] := Mod[n, DivisorSigma[0, n]]; Array[a, 105] (* _Jean-François Alcover_, Sep 19 2017 *)

%o (Haskell)

%o a054008 n = n `mod` a000005 n  -- _Reinhard Zumkeller_, Sep 17 2014

%o (PARI) a(n) = n % numdiv(n); \\ _Michel Marcus_, Sep 19 2017

%o (Python)

%o from sympy import divisor_count

%o def A054008(n): return n%divisor_count(n) # _Chai Wah Wu_, Mar 14 2023

%Y Cf. A000005, A054009, A033950, A066708.

%K nonn

%O 1,6

%A _Asher Auel_, Jan 12 2000