A145337 a(n) = d(p(n)+1) - d(p(n)-1), where d(m) = the number of divisors of m, p(n) = the n-th prime.

1, 1, 1, 0, 2, -2, 1, 0, 4, 2, -2, -5, 0, -2, 6, 2, 8, -8, -2, 4, -8, 2, 8, 4, -6, -1, 0, 8, -4, -2, -4, 4, 0, 4, 6, -4, -8, -4, 12, 2, 14, -10, 6, -10, 3, 0, -10, 4, 8, -4, 4, 12, -14, 10, -1, 12, 10, -6, -8, -8, -2, 6, 0, 8, -12, 2, -10, -14, 8, 0, -4, 20, 2, -4, -4, 12, 10, -14, -7, -8

Offset: 0

Author

Leroy Quet, Oct 08 2008

Keywords

• sign

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A008328, A008329, A067889, A103664, A103665, A145338.

Programs

Maple

A000005 := proc(n) numtheory[tau](n) ; end:
A008328 := proc(n) A000005(ithprime(n)-1) ; end:
A008329 := proc(n) A000005(ithprime(n)+1) ; end:
A145337 := proc(n) A008329(n)-A008328(n) ; end: # R. J. Mathar, Oct 10 2008

Mathematica

DivisorSigma[0,#+1]-DivisorSigma[0,#-1]&/@Prime[Range[80]] (* Harvey P. Dale, Nov 01 2011 *)

Formula

a(n) = A008329(n) - A008328(n). - R. J. Mathar, Oct 10 2008

Extensions

More terms from R. J. Mathar and Ray Chandler, Oct 10 2008