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A327566
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Partial sums of the infinitary divisors sum function: a(n) = Sum_{k=1..n} isigma(k), where isigma is A049417.
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3
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1, 4, 8, 13, 19, 31, 39, 54, 64, 82, 94, 114, 128, 152, 176, 193, 211, 241, 261, 291, 323, 359, 383, 443, 469, 511, 551, 591, 621, 693, 725, 776, 824, 878, 926, 976, 1014, 1074, 1130, 1220, 1262, 1358, 1402, 1462, 1522, 1594, 1642, 1710, 1760, 1838, 1910, 1980
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OFFSET
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1,2
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COMMENTS
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Differs from A307159 at n >= 16.
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REFERENCES
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Steven R. Finch, Mathematical Constants II, Cambridge University Press, 2018, section 1.7.5, pp. 53-54.
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LINKS
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Amiram Eldar, Table of n, a(n) for n = 1..10000
Graeme L. Cohen and Peter Hagis, Jr., Arithmetic functions associated with infinitary divisors of an integer, International Journal of Mathematics and Mathematical Sciences, Vol. 16, No. 2 (1993), pp. 373-383.
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FORMULA
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a(n) ~ c * n^2, where c = 0.730718... (A327574).
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MATHEMATICA
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f[p_, e_] := p^(2^(-1 + Position[Reverse @ IntegerDigits[e, 2], _?(# == 1 &)])); isigma[1] = 1; isigma[n_] := Times @@ (Flatten @ (f @@@ FactorInteger[n]) + 1); Accumulate[Array[isigma, 52]]
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CROSSREFS
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Cf. A049417 (isigma), A327574.
Cf. A024916 (all divisors), A064609 (unitary), A307042 (exponential), A307159 (bi-unitary).
Sequence in context: A034856 A183865 A064609 * A307159 A312212 A312213
Adjacent sequences: A327563 A327564 A327565 * A327567 A327568 A327569
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KEYWORD
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nonn
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AUTHOR
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Amiram Eldar, Sep 17 2019
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STATUS
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approved
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