A090502 Numbers k such that tau(k) = tau(k-1) + tau(k+1).

6, 20, 28, 32, 52, 56, 68, 152, 174, 176, 184, 186, 208, 212, 248, 266, 268, 272, 292, 322, 328, 338, 464, 470, 472, 476, 518, 534, 536, 578, 582, 585, 590, 602, 606, 650, 656, 658, 666, 670, 686, 710, 754, 772, 788, 790, 804, 814, 836, 846, 848, 894, 988

Offset: 1

Author

Amarnath Murthy, Dec 05 2003

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..4000
• Vaclav Kotesovec, Plot of a(n)/n for n = 1..1000000
• Vaclav Kotesovec, Plot of a(n)/(n*log(log(n))) for n = 1..1000000

Crossrefs

Cf. A074757.

Programs

Mathematica

Select[Range[1000],DivisorSigma[0,#]==DivisorSigma[0,#-1]+ DivisorSigma[ 0,#+1]&] (* Harvey P. Dale, Feb 27 2012 *)
Flatten[Position[Partition[DivisorSigma[0,Range[1000]],3,1],?(#[[2]]==#[[1]]+#[[3]]&),1,Heads->False]]+1 (* Much faster than the above Mathematica program because tau of each number only has to be calculated once. *) (* _Harvey P. Dale, Jan 03 2020 *)

PARI

is(n)=numdiv(n)==numdiv(n-1)+numdiv(n+1) \\ Charles R Greathouse IV, Apr 24 2013

Extensions

More terms from Ray Chandler, Dec 09 2003