A110756 a(n) = tau(N), where N = concatenation 1,2,3,...,n.
1, 6, 4, 4, 8, 28, 4, 24, 12, 8, 64, 32, 8, 8, 8, 12, 24, 48, 64, 192, 256, 64, 16, 48, 24, 160, 96, 64, 16, 128, 8, 48, 64, 4, 192, 120, 16, 16, 64, 384, 32, 128, 16, 48, 768, 128, 32, 192, 64, 768, 8, 32, 64, 1792, 32, 24, 64, 16, 16, 128, 8, 192, 24, 768, 64
Offset: 1
Examples
a(3) = tau(123) = 4.
Links
- Tyler Busby, Table of n, a(n) for n = 1..117
Programs
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Maple
A055642 := proc(n) 1+floor(log10(n)) ; end; A000005 := proc(n) numtheory[tau](n) ; end ; A007908 := proc(n) local a ; a := 1 ; for i from 2 to n do a := a*10^A055642(i)+i ; end; RETURN(a) ; end; A110756 := proc(n) A000005(A007908(n)) ; end; for n from 1 to 50 do printf("%d %d ",n,A110756(n)) ; od ; # R. J. Mathar, Feb 10 2007
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Mathematica
Table[DivisorSigma[0,FromDigits[Flatten[IntegerDigits/@Range[n]]]],{n,60}] (* Harvey P. Dale, Apr 01 2024 *)
Formula
Extensions
More terms from R. J. Mathar, Feb 10 2007
More terms from David Wasserman, Dec 22 2008
a(57)-a(65) from Jinyuan Wang, May 23 2020