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A307159
Partial sums of the bi-unitary divisors sum function: Sum_{k=1..n} bsigma(k), where bsigma is A188999.
5
1, 4, 8, 13, 19, 31, 39, 54, 64, 82, 94, 114, 128, 152, 176, 203, 221, 251, 271, 301, 333, 369, 393, 453, 479, 521, 561, 601, 631, 703, 735, 798, 846, 900, 948, 998, 1036, 1096, 1152, 1242, 1284, 1380, 1424, 1484, 1544, 1616, 1664, 1772, 1822, 1900, 1972, 2042
OFFSET
1,2
REFERENCES
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.
LINKS
László Tóth, Alternating sums concerning multiplicative arithmetic functions, Journal of Integer Sequences, Vol. 20 (2017), Article 17.2.1, section 4.13.
FORMULA
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).
MATHEMATICA
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]]
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Mar 27 2019
STATUS
approved