A138046 Positive integers k such that (d(k+1) - d(k)) * (-1)^k is positive, where d(k) = the number of positive divisors of k.
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
Offset: 1
Keywords
Links
- Muniru A Asiru, Table of n, a(n) for n = 1..10000
Crossrefs
Cf. A138047.
Programs
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GAP
Filtered([1..1000],n->IsPosInt((Tau(n+1)-Tau(n))*(-1)^n)); # Muniru A Asiru, May 27 2018
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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, 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
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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PARI
isok(n) = (numdiv(n+1) - numdiv(n))*(-1)^n > 0; \\ Michel Marcus, May 27 2018
Extensions
More terms from Emeric Deutsch, Mar 06 2008
More terms from R. J. Mathar and Robert G. Wilson v, Mar 23 2008
Comments