A090502 - OEIS

%I #25 Feb 24 2024 01:08:11

%S 6,20,28,32,52,56,68,152,174,176,184,186,208,212,248,266,268,272,292,

%T 322,328,338,464,470,472,476,518,534,536,578,582,585,590,602,606,650,

%U 656,658,666,670,686,710,754,772,788,790,804,814,836,846,848,894,988

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

%H Vincenzo Librandi, <a href="/A090502/b090502.txt">Table of n, a(n) for n = 1..4000</a>

%H Vaclav Kotesovec, <a href="/A090502/a090502.jpg">Plot of a(n)/n for n = 1..1000000</a>

%H Vaclav Kotesovec, <a href="/A090502/a090502_1.jpg">Plot of a(n)/(n*log(log(n))) for n = 1..1000000</a>

%t Select[Range[1000],DivisorSigma[0,#]==DivisorSigma[0,#-1]+ DivisorSigma[ 0,#+1]&] (* _Harvey P. Dale_, Feb 27 2012 *)

%t 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 *)

%o (PARI) is(n)=numdiv(n)==numdiv(n-1)+numdiv(n+1) \\ _Charles R Greathouse IV_, Apr 24 2013

%Y Cf. A074757.

%K nonn

%O 1,1

%A _Amarnath Murthy_, Dec 05 2003

%E More terms from _Ray Chandler_, Dec 09 2003