A139695 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.

1, 2, 6, 64, 121, 128, 131, 196, 65536, 65541, 65572, 117649, 262144, 262148, 262192, 279841, 287296, 287299, 287744, 292681, 4194304, 4194319, 4194325, 70368744177664, 2384185791015625, 2384185791015648, 2384185791085568

Offset

1,2

Comments

a(24) > 1400000000. - Robert G. Wilson v, Jun 06 2008

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

Links

Ray Chandler, Table of n, a(n) for n=1..89

Maple

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

Mathematica

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}]

Crossrefs

Cf. A139696.

Sequence in context: A145756 A030170 A082640 * A347949 A241590 A052522

Adjacent sequences: A139692 A139693 A139694 * A139696 A139697 A139698

Keyword

nonn

Author

Leroy Quet, Apr 29 2008, Jun 14 2008

Extensions

a(10)-a(20) from R. J. Mathar, May 04 2008

a(21)-a(23) from Robert G. Wilson v, Jun 05 2008

a(24)-a(27) from Ray Chandler, Jul 08 2009

Status

approved