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A307159 Partial sums of the bi-unitary divisors sum function: Sum_{k=1..n} bsigma(k), where bsigma is A188999. 4
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 (list; graph; refs; listen; history; text; internal format)
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

Amiram Eldar, Table of n, a(n) for n = 1..10000

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

Cf. A024916, A064609, A188999, A306069, A307042, A307160.

Sequence in context: A183865 A064609 A327566 * A312212 A312213 A312214

Adjacent sequences:  A307156 A307157 A307158 * A307160 A307161 A307162

KEYWORD

nonn

AUTHOR

Amiram Eldar, Mar 27 2019

STATUS

approved

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Last modified August 3 05:55 EDT 2020. Contains 336197 sequences. (Running on oeis4.)