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A138046
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Positive integers k such that (d(k+1) - d(k)) * (-1)^k is positive, where d(k) = the number of positive divisors of k.
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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
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OFFSET
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1,1
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COMMENTS
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The number of terms < 10^m, for m >= 1: 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, Mar 23 2008
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LINKS
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MAPLE
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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, Mar 06 2008
A051950 := proc(n) numtheory[tau](n)-numtheory[tau](n-1) ; 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+1) > 0 then RETURN(a) ; fi ; od: fi ; end: seq(A138046(n), n=1..80) ; # R. J. Mathar, Mar 31 2008
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MATHEMATICA
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f[n_] := (DivisorSigma[0, n + 1] - DivisorSigma[0, n])*(-1)^n; Select[ Range@ 565, f@# > 0 &] (* Robert G. Wilson v, Mar 23 2008 *)
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PROG
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(GAP) Filtered([1..1000], n->IsPosInt((Tau(n+1)-Tau(n))*(-1)^n)); # Muniru A Asiru, May 27 2018
(PARI) isok(n) = (numdiv(n+1) - numdiv(n))*(-1)^n > 0; \\ Michel Marcus, May 27 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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