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A243018
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Numbers k such that Sum_{i=1..k} phi(i) is divisible by Sum_{i=1..k} d(i), where phi(i) is the Euler totient function of i (A000010), and d(i) is the number of divisors of i (A000005).
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0
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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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FORMULA
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EXAMPLE
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phi(1) + phi(2) + phi(3) + phi(4) + phi(5) = 1 + 1 + 2 + 2 + 4 = 10;
d(1) + d(2) + d(3) + d(4) + d(5) = 1 + 2 + 2 + 3 + 2 = 10;
Finally 10 / 10 = 1.
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MAPLE
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with(numtheory):P:=proc(q) local a, b, n; a:=0; b:=0;
for n from 1 to q do a:=a+tau(n); b:=b+phi(n);
if type(b/a, integer) then print(n); fi; od; end: P(10^10);
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PROG
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(PARI) lista(nn) = {se = 0; sn = 0; for (n=1, nn, se += eulerphi(n); sn += numdiv(n); if (se % sn == 0, print1(n, ", ")); ); } \\ Michel Marcus, Nov 01 2014
(Magma) [n:n in [1..1000]| IsIntegral(&+[EulerPhi(m):m in [1..n]]/&+[NumberOfDivisors(m):m in [1..n]])] ; // Marius A. Burtea, Mar 25 2019
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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