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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.
4
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
1,1
COMMENTS
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
LINKS
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
MATHEMATICA
f[n_] := (DivisorSigma[0, n + 1] - DivisorSigma[0, n])*(-1)^n; Select[ Range@ 565, f@# > 0 &] (* Robert G. Wilson v, Mar 23 2008 *)
PROG
(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
CROSSREFS
Cf. A138047.
Sequence in context: A348923 A348922 A179007 * A324367 A140276 A140277
KEYWORD
nonn
AUTHOR
Leroy Quet, Mar 02 2008
EXTENSIONS
More terms from Emeric Deutsch, Mar 06 2008
More terms from R. J. Mathar and Robert G. Wilson v, Mar 23 2008
STATUS
approved