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A103116
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a(n) = Sum_{i=1..n} (n-i+1)*phi(i).
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4
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0, 1, 3, 7, 13, 23, 35, 53, 75, 103, 135, 177, 223, 281, 345, 417, 497, 593, 695, 815, 943, 1083, 1233, 1405, 1585, 1785, 1997, 2227, 2469, 2739, 3017, 3325, 3649, 3993, 4353, 4737, 5133, 5565, 6015, 6489, 6979, 7509, 8051, 8635, 9239, 9867, 10517, 11213, 11925
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OFFSET
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0,3
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LINKS
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FORMULA
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G.f.: (1/(1 - x)^2)*Sum_{k>=1} mu(k)*x^k/(1 - x^k)^2. - Ilya Gutkovskiy, Mar 16 2017
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MAPLE
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b:= proc(n) option remember; `if`(n<1, [0$2],
(p-> p+[numtheory[phi](n), p[1]])(b(n-1)))
end:
a:= n-> b(n+1)[2]:
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MATHEMATICA
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PROG
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(Magma)
A103116:= func< n | n eq 0 select 0 else (&+[(n-j+1)*EulerPhi(j): j in [1..n]]) >;
(SageMath)
@CachedFunction
def A103116(n): return sum( (n-j+1)*euler_phi(j) for j in range(1, 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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