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A070966
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a(n) = Sum_{k|n, k<=sqrt(n)} phi(k); where the sum is over the positive divisors, k, of n, which are <= the square root of n; and phi(k) is the Euler totient function.
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3
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1, 1, 1, 2, 1, 2, 1, 2, 3, 2, 1, 4, 1, 2, 3, 4, 1, 4, 1, 4, 3, 2, 1, 6, 5, 2, 3, 4, 1, 8, 1, 4, 3, 2, 5, 8, 1, 2, 3, 8, 1, 6, 1, 4, 7, 2, 1, 8, 7, 6, 3, 4, 1, 6, 5, 10, 3, 2, 1, 12, 1, 2, 9, 8, 5, 6, 1, 4, 3, 12, 1, 12, 1, 2, 7, 4, 7, 6, 1, 12, 9, 2, 1, 14, 5, 2, 3, 8, 1, 16, 7, 4, 3, 2, 5, 12, 1, 8, 9, 12
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OFFSET
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1,4
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LINKS
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FORMULA
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EXAMPLE
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a(30) = phi(1) + phi(2) + phi(3) + phi(5) = 1 + 1 + 2 + 4 = 8 because 1, 2, 3 and 5 are the positive divisors of 30 which are <= sqrt(30).
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MAPLE
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local a, k ;
a := 0 ;
for k in numtheory[divisors](n) do
if k^2 <= n then
a := a+numtheory[phi](k) ;
end if;
end do:
a ;
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PROG
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(PARI) a(n) = sumdiv(n, d, eulerphi(d)*(d^2 <= n)); \\ Michel Marcus, Dec 19 2017
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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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