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%I #9 Sep 30 2019 04:05:13
%S 1,2,4,7,11,13,19,22,30,34,44,50,62,68,76,91,107,115,133,145,157,167,
%T 189,195,219,231,247,265,293,301,331,346,366,382,406,430,466,484,508,
%U 520,560,572,614,644,676,698,744,774,822,846,878,914,966,982,1022,1040
%N Partial sums of an infinitary analog of Euler's phi function: a(n) = Sum_{k=1..n} iphi(k), where iphi is A091732.
%D Steven R. Finch, Mathematical Constants II, Cambridge University Press, 2018, section 1.7.5, pp. 53-54.
%H Amiram Eldar, <a href="/A327572/b327572.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 = 0.328935... (A327575).
%t f[p_, e_] := p^(2^(-1 + Position[Reverse @ IntegerDigits[e, 2], _?(# == 1 &)])); iphi[1] = 1; iphi[n_] := Times @@ (Flatten @ (f @@@ FactorInteger[n]) - 1); Accumulate[Array[iphi, 52]]
%Y Cf. A091732 (iphi), A327575.
%Y Cf. A002088 (sums of phi), A177754 (unitary), A306070 (bi-unitary).
%K nonn
%O 1,2
%A _Amiram Eldar_, Sep 17 2019
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