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A034496
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Sum of n-th powers of divisors of 8.
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5
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4, 15, 85, 585, 4369, 33825, 266305, 2113665, 16843009, 134480385, 1074791425, 8594130945, 68736258049, 549822930945, 4398314962945, 35185445863425, 281479271743489, 2251816993685505, 18014467229220865
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OFFSET
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0,1
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COMMENTS
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Conjecture: No primes in this sequence (checked for first 10000 terms). [Artur Jasinski, Sep 23 2008]
All terms are composite because a(n) = (1 + 2^n)*(1 + 4^n). [T. D. Noe, Apr 26 2010]
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LINKS
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FORMULA
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G.f.: (4 - 45*x + 140*x^2 - 120*x^3)/((1 - 8*x)*(1 - 4*x)*(1 - 2*x)*(1 - x)). [Bruno Berselli, Apr 17 2014]
a(n) = (2^(4*n) - 1)/( 2^n - 1) = 1 + 2^n + 4^n + 8^n. Exp( Sum_{n >= 1} a(n)*x^n/n ) = 1 + 15*x + 155*x^2 + 1395*x^3 + ... is the o.g.f. for the 3rd subdiagonal of triangle A022166, essentially A006096. - Peter Bala, Apr 07 2015
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MATHEMATICA
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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