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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
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OFFSET
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1,2
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COMMENTS
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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.
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LINKS
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FORMULA
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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
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EXAMPLE
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a(7) = 1 + 1 + 2 + 3 + 4 + 2 + 6 = 19.
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MATHEMATICA
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uphi[1] = 1; uphi[n_] := Times @@ (-1 + Power @@@ FactorInteger[n]); s = 0; Accumulate[Array[uphi, 60]] (* Amiram Eldar, Dec 18 2018*)
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CROSSREFS
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KEYWORD
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easy,nonn,changed
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AUTHOR
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STATUS
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approved
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