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%I #6 Dec 18 2018 15:07:35
%S 1,2,4,7,11,13,19,26,34,38,48,54,66,72,80,95,111,119,137,149,161,171,
%T 193,207,231,243,269,287,315,323,353,384,404,420,444,468,504,522,546,
%U 574,614,626,668,698,730,752,798,828,876,900,932,968,1020,1046,1086
%N Partial sums of A047994.
%C Partial sums of unitary totient (or unitary phi) function uphi(n). This is to A047994 as A002088 is to A000010. The subsequence of primes in the partial sum begins: 2, 7, 11, 13, 19, 137, 149, 193, 269, 353, 1523, 1543, 1609, 1657.
%H Eckford Cohen, <a href="https://doi.org/10.1007/BF01180473">Arithmetical functions associated with the unitary divisors of an integer</a>, Mathematische Zeitschrift, Vol. 74, No. 1 (1960), pp. 66-80.
%H R. Sitaramachandrarao and D. Suryanarayana, <a href="https://doi.org/10.1090/S0002-9939-1973-0319922-9">"On Sum_{n<=x} sigma*(n) and Sum_{n<=x} phi*(n)</a>, Proceedings of the American Mathematical Society, Vol. 41, No .1 (1973), pp. 61-66.
%F a(n) = Sum_{i=1..n} A047994(i).
%F a(n) ~ alpha * n^2/2 + O(n*log^2(n)) where alpha = Product_{p prime} (1 - 1/(p*(p+1))) = 0.704442... (A065463). - _Amiram Eldar_, Dec 18 2018
%e a(7) = 1 + 1 + 2 + 3 + 4 + 2 + 6 = 19.
%t uphi[1] = 1; uphi[n_] := Times @@ (-1 + Power @@@ FactorInteger[n]); s = 0; Accumulate[Array[uphi, 60]] (* _Amiram Eldar_, Dec 18 2018*)
%Y Cf. A000010, A002088, A003271, A047994, A065463.
%K easy,nonn
%O 1,2
%A _Jonathan Vos Post_, May 12 2010
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