A138047 Positive integers n such that (d(n+1) - d(n)) * (-1)^n is nonnegative, where d(n) = the number of positive divisors of n.

2, 14, 21, 26, 33, 34, 38, 44, 45, 57, 62, 74, 75, 81, 85, 86, 93, 94, 98, 104, 105, 116, 117, 118, 122, 133, 134, 135, 141, 142, 145, 146, 147, 158, 164, 165, 171, 177, 188, 189, 194, 201, 202, 205, 206, 213, 214, 217, 218, 225, 230, 231, 242, 243, 244, 253

Offset: 1

Author

Leroy Quet, Mar 02 2008

Keywords

• nonn

Crossrefs

Cf. A138046, A005237.

Programs

Maple

with(numtheory): a:=proc(n) if 0<=(-1)^n*(tau(n+1)-tau(n)) then n else end if end proc: seq(a(n),n=1..240); # Emeric Deutsch, Mar 06 2008
A051950 := proc(n) numtheory[tau](n)-numtheory[tau](n+1) ; end: A138047 := proc(n) option remember ; local a; if n = 1 then 2 ; else for a from A138047(n-1)+1 do if (-1)^a*A051950(a+1) >= 0 then RETURN(a) ; fi ; od: fi ; end: seq(A138047(n),n=1..80) ; # R. J. Mathar, Mar 31 2008

Mathematica

Select[Range[500], (DivisorSigma[0, # + 1] - DivisorSigma[0, # ])*(-1)^# > -1 &] (* Stefan Steinerberger, Mar 03 2008 *)

Formula

Union of the terms of A138046 and A005237.

Extensions

More terms from Stefan Steinerberger and Emeric Deutsch, Mar 03 2008

More terms from R. J. Mathar, Mar 31 2008