A139695 - OEIS

%I #15 Jun 13 2018 23:07:09

%S 1,2,6,64,121,128,131,196,65536,65541,65572,117649,262144,262148,

%T 262192,279841,287296,287299,287744,292681,4194304,4194319,4194325,

%U 70368744177664,2384185791015625,2384185791015648,2384185791085568

%N a(1)=1. a(n) = the smallest integer > a(n-1) such that |d(a(n)) - d(a(n-1))| = n-1, where d(m) = the number of positive divisors of m.

%C a(24) > 1400000000. - _Robert G. Wilson v_, Jun 06 2008

%C If n-1 >= d(a(n-1)), then d(a(n)) must be n-1 + d(a(n-1)).

%H Ray Chandler, <a href="/A139695/b139695.txt">Table of n, a(n) for n=1..89</a>

%p A139695 := proc(n) option remember ; local a,aprev; if n = 1 then 1; else aprev := A139695(n-1) ; for a from aprev+1 do if abs(numtheory[tau](a)-numtheory[tau](aprev)) = n-1 then RETURN(a) ; fi ; od: fi ; end: for n from 1 do print(A139695(n)) ; od: # _R. J. Mathar_, May 04 2008

%t f[1] = 1; f[n_] := f[n] = Block[{da = DivisorSigma[0, f[n - 1]], k = f[n - 1] + 1}, While[ Abs[ DivisorSigma[0, k] - da] + 1 != n, k++; m = k]; k]; Do[ Print[{n, f@n}], {n, 50}]

%Y Cf. A139696.

%K nonn

%O 1,2

%A _Leroy Quet_, Apr 29 2008, Jun 14 2008

%E a(10)-a(20) from _R. J. Mathar_, May 04 2008

%E a(21)-a(23) from _Robert G. Wilson v_, Jun 05 2008

%E a(24)-a(27) from _Ray Chandler_, Jul 08 2009