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1, 3, 4, 6, 9, 15, 24, 42, 72, 128, 227, 413, 748, 1378, 2539, 4721, 8801, 16511, 31043, 58637, 111014, 210872, 401429, 766151, 1465021, 2807197, 5387992, 10359000, 19945395, 38458185, 74248452, 143522118, 277737798, 538038784, 1043325199
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OFFSET
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0,2
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COMMENTS
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Partial sums of number of degree-n irreducible polynomials over GF(2). Partial sums of dimensions of free Lie algebras. Partial sums of number of n-bead necklaces with beads of 2 colors when turning over is not allowed and with primitive period n. Partial sums of number of binary Lyndon words of length n. The subsequence of primes in this partial sum begins: 3, 227, 2539, 4721, 1465021, 2807197. The subsequence from the underlying sequence in this partial sum begins: 1, 3, 6, 9, and then what?
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LINKS
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Table of n, a(n) for n=0..34.
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FORMULA
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a(n) = SUM[i=0..n] A001037 (i) = SUM[i=0..n] (1/i) SUM_{d divides i} mu(i/d) 2^i.
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EXAMPLE
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a(35) = 1 + 2 + 1 + 2 + 3 + 6 + 9 + 18 + 30 + 56 + 99 + 186 + 335 + 630 + 1161 + 2182 + 4080 + 7710 + 14532 + 27594 + 52377 + 99858 + 190557 + 364722 + 698870 + 1342176 + 2580795 + 4971008 + 9586395 + 18512790 + 35790267 + 69273666 + 134215680 + 260300986 + 505286415 + 981706806.
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CROSSREFS
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Cf. A001037, A058943 and A102569 for initial terms of underlying sequence. See also A058947, A011260, A059966, A000031 (n-bead necklaces but may have period dividing n).
Sequence in context: A147790 A048577 A107340 * A018830 A102934 A191699
Adjacent sequences: A173267 A173268 A173269 * A173271 A173272 A173273
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KEYWORD
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nonn
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AUTHOR
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Jonathan Vos Post, Feb 14 2010
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STATUS
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approved
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