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

1,1

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

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