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

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, -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, -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

Offset: 1

Author

Omar E. Pol, Jun 28 2009

Keywords

• easy
• sign

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000
• Omar E. Pol, Illustration: Divisors and pi(x)

Crossrefs

Cf. A000005, A001223, A161912.

Programs

Maple

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

Mathematica

With[{nn=90},#[[1]]-DivisorSigma[0,#[[2]]]&/@Thread[{Differences[Prime[ Range[ nn]]],Range[nn-1]}]] (* Harvey P. Dale, Oct 01 2018 *)

Formula

a(n) = A001223(n) - A000005(n).

Extensions

More terms from R. J. Mathar, Jul 01 2009