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 A177754 Partial sums of A047994. 4
 1, 2, 4, 7, 11, 13, 19, 26, 34, 38, 48, 54, 66, 72, 80, 95, 111, 119, 137, 149, 161, 171, 193, 207, 231, 243, 269, 287, 315, 323, 353, 384, 404, 420, 444, 468, 504, 522, 546, 574, 614, 626, 668, 698, 730, 752, 798, 828, 876, 900, 932, 968, 1020, 1046, 1086 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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. LINKS Eckford Cohen, Arithmetical functions associated with the unitary divisors of an integer, Mathematische Zeitschrift, Vol. 74, No. 1 (1960), pp. 66-80. R. Sitaramachandrarao and D. Suryanarayana, "On Sum_{n<=x} sigma*(n) and Sum_{n<=x} phi*(n), Proceedings of the American Mathematical Society, Vol. 41, No .1 (1973), pp. 61-66. FORMULA a(n) = Sum_{i=1..n} A047994(i). 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 EXAMPLE a(7) = 1 + 1 + 2 + 3 + 4 + 2 + 6 = 19. MATHEMATICA uphi[1] = 1; uphi[n_] := Times @@ (-1 + Power @@@ FactorInteger[n]); s = 0; Accumulate[Array[uphi, 60]] (* Amiram Eldar, Dec 18 2018*) CROSSREFS Cf. A000010, A002088, A003271, A047994, A065463. Sequence in context: A307207 A165288 A327572 * A086795 A064690 A138766 Adjacent sequences:  A177751 A177752 A177753 * A177755 A177756 A177757 KEYWORD easy,nonn AUTHOR Jonathan Vos Post, May 12 2010 STATUS approved

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Last modified April 1 14:52 EDT 2020. Contains 333163 sequences. (Running on oeis4.)