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A161911 a(n) is the n-th difference between consecutive primes minus the number of divisors of n.

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%I A161911 #12 Feb 27 2019 02:50:53
%S A161911 0,0,0,1,0,0,0,0,3,-2,4,-2,0,0,2,1,0,0,2,-4,2,0,4,0,1,-2,0,-4,2,6,2,0,
%T A161911 -2,6,-2,-3,4,0,2,-2,0,2,0,-2,-4,8,10,-6,-1,-2,2,-4,8,-2,2,-2,-2,2,2,
%U A161911 -10,8,10,-2,-5,0,6,4,4,-2,-4,4,-4,4,2,-2,0,4,-4,6,0,-3,6,0,-6,0,2,4,-4
%N A161911 a(n) is the n-th difference between consecutive primes minus the number of divisors of n.
%H A161911 Harvey P. Dale, <a href="/A161911/b161911.txt">Table of n, a(n) for n = 1..1000</a>
%H A161911 Omar E. Pol, <a href="http://www.polprimos.com/imagenespub/polprdipi.jpg">Illustration: Divisors and pi(x)</a>
%F A161911 a(n) = A001223(n) - A000005(n).
%p A161911 A001223 := proc(n) ithprime(n+1)-ithprime(n) ; end: A000005 := proc(n) numtheory[tau](n) ; end: A161911 := proc(n) A001223(n)-A000005(n) ; end: seq(A161911(n),n=1..120) ; # _R. J. Mathar_, Jul 01 2009
%t A161911 With[{nn=90},#[[1]]-DivisorSigma[0,#[[2]]]&/@Thread[{Differences[Prime[ Range[ nn]]],Range[nn-1]}]] (* _Harvey P. Dale_, Oct 01 2018 *)
%Y A161911 Cf. A000005, A001223, A161912.
%K A161911 easy,sign
%O A161911 1,9
%A A161911 _Omar E. Pol_, Jun 28 2009
%E A161911 More terms from _R. J. Mathar_, Jul 01 2009