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A138046
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Positive integers n such that (d(n+1) - d(n)) * (-1)^n is positive, where d(n) = the number of positive divisors of n.
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4
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45, 62, 74, 81, 105, 117, 134, 146, 164, 165, 188, 194, 206, 225, 254, 261, 273, 274, 278, 284, 297, 314, 315, 325, 333, 345, 356, 357, 362, 385, 386, 398, 404, 405, 422, 428, 435, 441, 454, 458, 465, 477, 482, 494, 495, 513, 524, 525, 538, 554, 555, 561
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| The number of terms < 10^n: 0,4,104,1320,15000,162705,..., . The smallest term which is the beginning of n consecutive terms: 45,164,625,2274,30481,150992,624963,726421,..., . - Robert G. Wilson v.
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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..500); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 06 2008
A051950 := proc(n) numtheory[tau](n+1)-numtheory[tau](n) ; end: A138046 := proc(n) option remember ; local a; if n = 1 then 45 ; else for a from A138046(n-1)+1 do if (-1)^a*A051950(a) > 0 then RETURN(a) ; fi ; od: fi ; end: seq(A138046(n), n=1..80) ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 31 2008
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MATHEMATICA
| f[n_] := (DivisorSigma[0, n + 1] - DivisorSigma[0, n])*(-1)^n; Select[ Range@ 565, f@# > 0 &] (* Robert G. Wilson v *)
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CROSSREFS
| Cf. A138047.
Sequence in context: A206024 A151743 A179007 * A140276 A140277 A077646
Adjacent sequences: A138043 A138044 A138045 * A138047 A138048 A138049
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KEYWORD
| nonn
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AUTHOR
| Leroy Quet, Mar 02 2008
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EXTENSIONS
| More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 06 2008
More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl) and Robert G. Wilson v (rgwv(AT)rgwv.com), Mar 23 2008
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