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

1,1

Links

Table of n, a(n) for n=1..56.

Formula

Union of the terms of A138046 and A005237.

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 *)

Crossrefs

Cf. A138046, A005237.

Sequence in context: A187261 A101398 A131221 * A005237 A140578 A052213

Adjacent sequences: A138044 A138045 A138046 * A138048 A138049 A138050

Keyword

nonn

Author

Leroy Quet, Mar 02 2008

Extensions

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

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

Status

approved