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%I #22 Apr 25 2020 11:15:52
%S 1,4,8,13,19,31,39,48,58,76,88,108,122,146,170,187,205,235,255,285,
%T 317,353,377,413,439,481,509,549,579,651,683,716,764,818,866,916,954,
%U 1014,1070,1124,1166,1262,1306,1366,1426,1498,1546,1614,1664,1742,1814,1884
%N Partial sums of A034448: sum of unitary divisors from 1 to n.
%H Harry J. Smith, <a href="/A064609/b064609.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = a(n-1) + A034448(n) = Sum_{j=1..n} usigma(j) where usigma(j) = A034448(j).
%F a(n) ~ Pi^2 * n^2 / (12*Zeta(3)). - _Vaclav Kotesovec_, Jan 11 2019
%t Accumulate@ Table[DivisorSum[n, # &, CoprimeQ[#, n/#] &], {n, 52}] (* _Michael De Vlieger_, Mar 18 2017 *)
%o (PARI) usigma(n)= { local(f,s=1); f=factor(n); for(i=1, matsize(f)[1], s*=1 + f[i, 1]^f[i, 2]); return(s) }
%o { a=0; for (n=1, 1000, a+=usigma(n); write("b064609.txt", n, " ", a) ) } \\ _Harry J. Smith_, Sep 20 2009
%o (Python)
%o from sympy.ntheory.factor_ import udivisor_sigma
%o def a(n): return sum(udivisor_sigma(j,1) for j in range(1,n + 1))
%o print([a(n) for n in range(1, 101)]) # _Indranil Ghosh_, Mar 18 2017
%Y Cf. A034448, A064611.
%K nonn
%O 1,2
%A _Labos Elemer_, Sep 24 2001
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