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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| 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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EXAMPLE
| a(3) = tau(12321) = 9.
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MAPLE
| 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 (mathar(AT)strw.leidenuniv.nl), Feb 10 2007
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CROSSREFS
| Cf. A110756, A110757, A110758, A110760.
Sequence in context: A111120 A100401 A004166 * A063750 A143225 A203600
Adjacent sequences: A110756 A110757 A110758 * A110760 A110761 A110762
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KEYWORD
| base,more,nonn
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AUTHOR
| Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Aug 11 2005
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EXTENSIONS
| More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 10 2007
a(21)-a(35) from Robert Gerbicz (robert.gerbicz(AT)gmail.com), Nov 27 2010
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