A327566 Partial sums of the infinitary divisors sum function: a(n) = Sum_{k=1..n} isigma(k), where isigma is A049417.

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

Offset

1,2

Comments

Differs from A307159 at n >= 16.

References

Steven R. Finch, Mathematical Constants II, Cambridge University Press, 2018, section 1.7.5, pp. 53-54.

Links

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.

Formula

a(n) ~ c * n^2, where c = 0.730718... (A327574).

Mathematica

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]]

Crossrefs

Cf. A049417 (isigma), A327574.

Cf. A024916 (all divisors), A064609 (unitary), A307042 (exponential), A307159 (bi-unitary).

Sequence in context: A362290 A183865 A064609 * A307159 A365697 A312212

Adjacent sequences: A327563 A327564 A327565 * A327567 A327568 A327569

Keyword

nonn

Author

Amiram Eldar, Sep 17 2019

Status

approved