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A138047
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Positive integers n such that (d(n+1) - d(n)) * (-1)^n is nonnegative, where d(n) = the number of positive divisors of n.
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2
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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FORMULA
| Union of the terms of A138046 and A005237.
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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 (deutsch(AT)duke.poly.edu), Mar 06 2008
A051950 := proc(n) numtheory[tau](n+1)-numtheory[tau](n) ; 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) >= 0 then RETURN(a) ; fi ; od: fi ; end: seq(A138047(n), n=1..80) ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 31 2008
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MATHEMATICA
| Select[Range[500], (DivisorSigma[0, # + 1] - DivisorSigma[0, # ])*(-1)^# > -1 &] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Mar 03 2008
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CROSSREFS
| Cf. A138046, A005237.
Sequence in context: A187261 A101398 A131221 * A005237 A140578 A052213
Adjacent sequences: A138044 A138045 A138046 * A138048 A138049 A138050
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KEYWORD
| nonn
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AUTHOR
| Leroy Quet Mar 02 2008
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EXTENSIONS
| More terms from Stefan Steinerberger (stefan.steinerberger(AT)gmail.com) and Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 03 2008
More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 31 2008
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