This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A090502 #25 Feb 24 2024 01:08:11 %S A090502 6,20,28,32,52,56,68,152,174,176,184,186,208,212,248,266,268,272,292, %T A090502 322,328,338,464,470,472,476,518,534,536,578,582,585,590,602,606,650, %U A090502 656,658,666,670,686,710,754,772,788,790,804,814,836,846,848,894,988 %N A090502 Numbers k such that tau(k) = tau(k-1) + tau(k+1). %H A090502 Vincenzo Librandi, <a href="/A090502/b090502.txt">Table of n, a(n) for n = 1..4000</a> %H A090502 Vaclav Kotesovec, <a href="/A090502/a090502.jpg">Plot of a(n)/n for n = 1..1000000</a> %H A090502 Vaclav Kotesovec, <a href="/A090502/a090502_1.jpg">Plot of a(n)/(n*log(log(n))) for n = 1..1000000</a> %t A090502 Select[Range[1000],DivisorSigma[0,#]==DivisorSigma[0,#-1]+ DivisorSigma[ 0,#+1]&] (* _Harvey P. Dale_, Feb 27 2012 *) %t A090502 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 A090502 (PARI) is(n)=numdiv(n)==numdiv(n-1)+numdiv(n+1) \\ _Charles R Greathouse IV_, Apr 24 2013 %Y A090502 Cf. A074757. %K A090502 nonn %O A090502 1,1 %A A090502 _Amarnath Murthy_, Dec 05 2003 %E A090502 More terms from _Ray Chandler_, Dec 09 2003