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A193553
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Sum of divisors of 4*n.
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20
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7, 15, 28, 31, 42, 60, 56, 63, 91, 90, 84, 124, 98, 120, 168, 127, 126, 195, 140, 186, 224, 180, 168, 252, 217, 210, 280, 248, 210, 360, 224, 255, 336, 270, 336, 403, 266, 300, 392, 378, 294, 480, 308, 372, 546, 360, 336, 508, 399, 465, 504, 434, 378, 600, 504, 504, 560, 450, 420, 744, 434, 480, 728, 511, 588, 720
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OFFSET
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1,1
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LINKS
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FORMULA
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a(n) = 3*sigma(2*n) - 2*sigma(n); the relation is the special case e=1, p=2 of the relation sigma(t^2*n) = (t+1)*sigma(t*n) - t*sigma(n) where t=p^e (p a prime).
G.f. is x times the logarithmic derivative of the g.f. of A182820.
a(2*n-1) = 7 * A008438(n) = 7 * sigma(2*n-1); special case of sigma(2^k*(2*n-1)) = (2^(k+1)-1) * sigma(2*n-1).
Sum_{k=1..n} a(k) = (11*Pi^2/24) * n^2 + O(n*log(n)). - Amiram Eldar, Dec 16 2022
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MATHEMATICA
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PROG
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(PARI) vector(66, n, sigma(4*n, 1))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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