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 A138046 Positive integers n such that (d(n+1) - d(n)) * (-1)^n is positive, where d(n) = the number of positive divisors of n. 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 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, Mar 23 2008 LINKS Muniru A Asiru, Table of n, a(n) for n = 1..10000 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 Adjacent sequences: A138043 A138044 A138045 * A138047 A138048 A138049 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

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Last modified November 29 15:30 EST 2022. Contains 358431 sequences. (Running on oeis4.)