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A108639
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a(n) = Sum_{k=1..n} sigma_{n-k}(k), where sigma_m(k) = Sum_{j|k} j^m.
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4
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1, 3, 6, 13, 29, 77, 229, 771, 2863, 11573, 50365, 234161, 1156039, 6031751, 33130187, 190929778, 1151198268, 7243777234, 47462906927, 323188163753, 2282922216819, 16701529748621, 126359471558613, 987316752551419
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OFFSET
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1,2
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COMMENTS
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LINKS
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EXAMPLE
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a(5) = 1^4 + (1^3 + 2^3) + (1^2 + 3^2) + (1^1 + 2^1 + 4^1) + (1^0 + 5^0) = 1 + 1 + 8 + 1 + 9 + 1 + 2 + 4 + 1 + 1 = 29.
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MAPLE
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with(numtheory): s:=proc(n, k) local div: div:=divisors(n): sum(div[j]^k, j=1..tau(n)) end: a:=n->sum(s(i, n-i), i=1..n): seq(a(n), n=1..27); # Emeric Deutsch, Jul 13 2005
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MATHEMATICA
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PROG
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(PARI) a(n) = sum(k=1, n, sigma(k, n-k)); \\ Michel Marcus, Dec 24 2017
(Magma)
A108639:= func< n | (&+[DivisorSigma(j, n-j): j in [0..n-1]]) >;
(SageMath)
def A108639(n): return sum(sigma(n-j, j) for j in range(n))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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