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 A110759 #49 Mar 04 2025 16:30:08
%S A110759 1,3,9,9,9,243,9,81,45,2,4,18,8,64,96,16,24,48,64,4,48,8,16,384,4,64,
%T A110759 640,4,16,768,16,512,144,64,64,448,8,48,192,16,64,96,8,64,896,128,64,
%U A110759 192,128,128,384,32,64,1280,16,64,192,16,24,192,32,16
%N A110759 a(n) = tau(N), where N = concatenation 1,2,3,...,n,...,3,2,1. E.g., for n = 4, N = 1234321.
%C A110759 First 9 terms are odd as corresponding N are perfect squares.
%C A110759 Factorization of the larger N values:
%C A110759 f(25) = 989931671244066864878631629*p53
%C A110759 f(26) = 7*3209*17627*1322221*554840431325362973971*p48
%C A110759 f(27) = 3^4*7*223*28807*108727*5439394515032275997*361855463775135800641*p34
%C A110759 f(28) = 149*p89
%C A110759 f(29) = 7*317310923*296879723071339*p72
%C A110759 f(30) = 3^2*7*167*761*133337*431911*273884231501*4950715302671*p58
%C A110759 f(31) = 827*1141296551*10940622359204560200188943089306257*p58
%C A110759 f(32) = 7*31*5537737*42583813*62231909*19871693507*1441602757913*15884064847039967*p44
%C A110759 f(33) = 3^2*7^2*281*743580875118413*177233764237488717892587862569137279765057*p50
%C A110759 f(34) = 197*509*17780359481*34117699655579*22315348168833851*p70
%C A110759 f(35) = 7*10243*73778819*217751506979*815234955828637451*p78
%F A110759 a(n) = A000005(A173426(n)). - _Georg Fischer_, Feb 28 2023
%e A110759 a(3) = tau(12321) = 9.
%p A110759 A055642 := proc(n) 1+floor(log10(n)) ; end; A000005 := proc(n) numtheory[tau](n) ; end ; rep := proc(n) local a ; a := 1 ; for i from 2 to n do a := a*10^A055642(i)+i ; end; for i from n-1 to 1 by -1 do a := a*10^A055642(i)+i ; end; RETURN(a) ; end; A110759 := proc(n) A000005(rep(n)) ; end; for n from 1 to 50 do printf("%d %d ",n,A110759(n)) ; od ; # _R. J. Mathar_, Feb 10 2007
%t A110759 Table[DivisorSigma[0,FromDigits[Join[Flatten[IntegerDigits/@Range[n]], Flatten[ IntegerDigits/@ Range[n-1,1,-1]]]]],{n,40}] (* _Harvey P. Dale_, Nov 17 2017 *)
%Y A110759 Cf. A000005, A110756, A110757, A110758, A110760, A173426.
%K A110759 nonn,base,more
%O A110759 1,2
%A A110759 _Amarnath Murthy_, Aug 11 2005
%E A110759 More terms from _R. J. Mathar_, Feb 10 2007
%E A110759 a(21)-a(35) from _Robert Gerbicz_, Nov 27 2010
%E A110759 a(36)-a(44) from _Jinyuan Wang_, May 17 2020
%E A110759 a(45)-a(58) from _Tyler Busby_, Feb 13 2023
%E A110759 a(59)-a(62) from _Tyler Busby_, Mar 04 2025