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A065417
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Exponents in expansion of rank-2 Artin constant product(1-1/(p^3-p^2), p=prime) as a product zeta(n)^(-a(n)).
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2
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0, 0, 1, 1, 1, 1, 2, 2, 3, 4, 6, 7, 11, 14, 20, 27, 39, 52, 75, 102, 145, 201, 286, 397, 565, 791, 1123, 1581, 2248, 3173, 4517, 6399, 9112, 12945, 18457, 26270, 37502, 53478, 76416, 109146, 156135, 223301, 319764, 457884, 656288, 940795, 1349671, 1936620
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OFFSET
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1,7
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COMMENTS
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Inverse Euler transform of A078012. (The inverse of 1-1/(p^3-p^2) is p^2(p-1)/(p^3-p^2-1) = 1-1/(1+p^2-p^3). Setting 1/p=x gives (1-x)/(1-x-x^3), the g.f. of A078012.) [From R. J. Mathar, Jul 26 2010]
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LINKS
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Table of n, a(n) for n=1..48.
R. J. Mathar, Hardy-Littlewood constants embedded into infinite products over all positive integers, sequence gamma_{2,j}^(A).
G. Niklasch, Some number theoretical constants: 1000-digit values [Cached copy]
Index entries for sequences related to Artin's conjecture
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EXAMPLE
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x^3 + x^4 + x^5 + x^6 + 2*x^7 + 2*x^8 + 3*x^9 + 4*x^10 + 6*x^11 + 7*x^12 + ...
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MAPLE
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Contribution from R. J. Mathar, Jul 26 2010: (Start)
read("transforms") ;
A078012 := proc(n) option remember; if n <3 then op(n+1, [1, 0, 0]) ; else procname(n-1)+procname(n-3) ; end if; end proc:
a078012 := [seq(A078012(n), n=1..80)] ; EULERi(%) ; (End)
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CROSSREFS
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Cf. A065414.
Sequence in context: A115593 A094860 A213816 * A005860 A114541 A077114
Adjacent sequences: A065414 A065415 A065416 * A065418 A065419 A065420
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane, Nov 15 2001
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EXTENSIONS
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More terms from R. J. Mathar, Jul 26 2010
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STATUS
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approved
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