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 A131383 Total digital sum of n: sum of the digital sums of n for all the bases 1 to n (a 'digital sumorial'). 5
 1, 3, 6, 8, 13, 16, 23, 25, 30, 35, 46, 46, 59, 66, 75, 74, 91, 91, 110, 112, 125, 136, 159, 152, 169, 182, 195, 199, 228, 223, 254, 253, 274, 291, 316, 297, 334, 353, 378, 373, 414, 409, 452, 460, 475, 498, 545, 520, 557, 565, 598, 608, 661, 652, 693, 690 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Sums of rows of the triangle in A138530. - Reinhard Zumkeller, Mar 26 2008 LINKS Hieronymus Fischer, Table of n, a(n) for n = 1..10000 Eric Weisstein's World of Mathematics, Digit Sum FORMULA a(n) = n^2-sum{k>0, sum{2<=p<=n, (p-1)*floor(n/p^k)}}. a(n) = n^2-sum{2<=p<=n, (p-1)*sum{01, sum{2<=p<=n, (p-1)*floor(n/p^k)}}. a(n) = A004125(n)+A006218(n)-sum{k>1, sum{2<=p<=n, (p-1)*floor(n/p^k)}}. Asymptotic behavior: a(n) = (1-Pi^2/12)*n^2 + O(n*log(n)) = A004125(n) + A006218(n) + O(n*log(n)). Lim a(n)/n^2 = 1 - Pi^2/12 for n-->oo. G.f.: (1/(1-x))*(x(1+x)/(1-x)^2-sum{k>0,sum{j>1,(j-1)*x^(j^k)/(1-x^(j^k))}= }). Also: (1/(1-x))*(x(1+x)/(1-x)^2-sum{m>1, sum{10,j^(1/k) is integer, j^(1/k)-1}}*x^m}). a(n) = n^2-sum{10,sum{1

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Last modified December 16 01:36 EST 2017. Contains 296063 sequences.