|
%I #10 Sep 30 2019 04:04:57
%S 1,4,8,13,19,31,39,54,64,82,94,114,128,152,176,193,211,241,261,291,
%T 323,359,383,443,469,511,551,591,621,693,725,776,824,878,926,976,1014,
%U 1074,1130,1220,1262,1358,1402,1462,1522,1594,1642,1710,1760,1838,1910,1980
%N Partial sums of the infinitary divisors sum function: a(n) = Sum_{k=1..n} isigma(k), where isigma is A049417.
%C Differs from A307159 at n >= 16.
%D Steven R. Finch, Mathematical Constants II, Cambridge University Press, 2018, section 1.7.5, pp. 53-54.
%H Amiram Eldar, <a href="/A327566/b327566.txt">Table of n, a(n) for n = 1..10000</a>
%H Graeme L. Cohen and Peter Hagis, Jr., <a href="http://dx.doi.org/10.1155/S0161171293000456">Arithmetic functions associated with infinitary divisors of an integer</a>, International Journal of Mathematics and Mathematical Sciences, Vol. 16, No. 2 (1993), pp. 373-383.
%F a(n) ~ c * n^2, where c = 0.730718... (A327574).
%t 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]]
%Y Cf. A049417 (isigma), A327574.
%Y Cf. A024916 (all divisors), A064609 (unitary), A307042 (exponential), A307159 (bi-unitary).
%K nonn
%O 1,2
%A _Amiram Eldar_, Sep 17 2019
|
