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A020516
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Sum of n-th powers of divisors of 64.
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4
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7, 127, 5461, 299593, 17895697, 1108378657, 69810262081, 4432676798593, 282578800148737, 18049651735527937, 1154048505100108801, 73823022692637345793, 4723519685917965029377, 302268352895954163081217
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OFFSET
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0,1
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COMMENTS
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7th cyclotomic polynomial evaluated at powers of 2.
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LINKS
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FORMULA
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G.f.: (-7+762 x-26670 x^2+377952 x^3-2267712 x^4+5462016 x^5-4161536 x^6)/(-1+127 x-5334 x^2+94488 x^3-755904 x^4+2731008 x^5-4161536 x^6+2097152 x^7). - Harvey P. Dale, Mar 21 2011
a(n) = (2^(7*n) - 1)/( 2^n - 1). Exp( Sum_{n >= 1} a(n)*x^n/n ) = 1 + 127*x + 10795*x^2 + ... is the o.g.f. for the 6th subdiagonal of triangle A022166, essentially A022189. - Peter Bala, Apr 07 2015
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MAPLE
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with(numtheory, cyclotomic):seq(cyclotomic(7, 2^i), i=0..24);
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MATHEMATICA
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Total[#^Range[0, 15]&/@Divisors[64]] (* Harvey P. Dale, Mar 21 2011 *)
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PROG
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(Magma) [&+[Divisors(64)[i]^n: i in [1..7]]: n in [0..15]]; // Vincenzo Librandi, Apr 17 2014
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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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