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%I #9 Jul 23 2019 07:54:07
%S 1,4,8,13,19,31,39,54,64,82,94,114,128,152,176,203,221,251,271,301,
%T 333,369,393,453,479,521,561,601,631,703,735,798,846,900,948,998,1036,
%U 1096,1152,1242,1284,1380,1424,1484,1544,1616,1664,1772,1822,1900,1972,2042
%N Partial sums of the bi-unitary divisors sum function: Sum_{k=1..n} bsigma(k), where bsigma is A188999.
%D D. Suryanarayana and M. V. Subbarao, Arithmetical functions associated with the biunitary k-ary divisors of an integer, Indian J. Math., Vol. 22 (1980), pp. 281-298.
%H Amiram Eldar, <a href="/A307159/b307159.txt">Table of n, a(n) for n = 1..10000</a>
%H László Tóth, <a href="http://emis.ams.org/journals/JIS/VOL20/Toth/toth25.html">Alternating sums concerning multiplicative arithmetic functions</a>, Journal of Integer Sequences, Vol. 20 (2017), Article 17.2.1, section 4.13.
%F a(n) ~ c * n^2, where c = (zeta(2)*zeta(3)/2) * Product_{p}(1 - 2/p^3 + 1/p^4 + 1/p^5 - 1/p^6) (A307160).
%t fun[p_,e_] := If[OddQ[e],(p^(e+1)-1)/(p-1),(p^(e+1)-1)/(p-1)-p^(e/2)]; bsigma[1] = 1; bsigma[n_] := Times @@ (fun @@@ FactorInteger[n]); Accumulate[Array[bsigma, 60]]
%Y Cf. A024916, A064609, A188999, A306069, A307042, A307160.
%K nonn
%O 1,2
%A _Amiram Eldar_, Mar 27 2019