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%I #18 Oct 07 2017 07:30:03
%S 0,0,0,0,1,1,1,0,0,1,3,3,1,0,0,2,3,3,3,1,0,1,5,4,0,0,1,3,5,5,3,1,0,0,
%T 4,6,1,0,3,5,5,5,3,0,1,1,7,6,2,1,1,3,5,3,3,3,0,1,9,9,1,1,0,2,3,5,3,1,
%U 3,5,9,9,1,1,0,1,3,5,7,4,0,1,9,7,0,0,3,5,9,7,1,1,0,0,7,9,3,0,2,6,5,5,5,0,3
%N Number of natural numbers between d(n) and d(n+1), where d(n) denotes the number of divisors of n.
%H Antti Karttunen, <a href="/A130632/b130632.txt">Table of n, a(n) for n = 1..20000</a>
%F a(n) = max(0, |A051950(n+1)| - 1). - _R. J. Mathar_, Jun 28 2010
%p A051950 := proc(n) if n = 0 then 1; else numtheory[tau](n+1)-numtheory[tau](n) ; end if; end proc:
%p A130632 := proc(n) local g ; g := abs(A051950(n)) ; max(0,g-1) ; end proc:
%p seq(A130632(n),n=1..80) ;
%p # _R. J. Mathar_, Jun 28 2010
%o (PARI) a(n) = max(0, abs(numdiv(n+1)-numdiv(n))-1); \\ _Michel Marcus_, Aug 24 2015
%Y Cf. A000005, A051950.
%K nonn
%O 1,11
%A _Giovanni Teofilatto_, Aug 11 2007
%E More terms from _R. J. Mathar_, Jun 28 2010
%E Extended up to a(105) by _Antti Karttunen_, Oct 07 2017
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