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A110759
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a(n) = tau(N), where N = concatenation 1,2,3,...,n,...,3,2,1. E.g., for n = 4, N = 1234321.
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5
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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, 640, 4, 16, 768, 16, 512, 144, 64, 64, 448, 8, 48, 192, 16, 64, 96, 8, 64, 896, 128, 64, 192, 128, 128, 384, 32, 64, 1280, 16, 64, 192, 16
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OFFSET
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1,2
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COMMENTS
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First 9 terms are odd as corresponding N are perfect squares.
Factorization of the larger N values:
f(25) = 989931671244066864878631629*p53
f(26) = 7*3209*17627*1322221*554840431325362973971*p48
f(27) = 3^4*7*223*28807*108727*5439394515032275997*361855463775135800641*p34
f(28) = 149*p89
f(29) = 7*317310923*296879723071339*p72
f(30) = 3^2*7*167*761*133337*431911*273884231501*4950715302671*p58
f(31) = 827*1141296551*10940622359204560200188943089306257*p58
f(32) = 7*31*5537737*42583813*62231909*19871693507*1441602757913*15884064847039967*p44
f(33) = 3^2*7^2*281*743580875118413*177233764237488717892587862569137279765057*p50
f(34) = 197*509*17780359481*34117699655579*22315348168833851*p70
f(35) = 7*10243*73778819*217751506979*815234955828637451*p78
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LINKS
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FORMULA
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EXAMPLE
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a(3) = tau(12321) = 9.
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MAPLE
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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
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MATHEMATICA
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Table[DivisorSigma[0, FromDigits[Join[Flatten[IntegerDigits/@Range[n]], Flatten[ IntegerDigits/@ Range[n-1, 1, -1]]]]], {n, 40}] (* Harvey P. Dale, Nov 17 2017 *)
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CROSSREFS
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KEYWORD
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nonn,base,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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