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A029935
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Sum phi(d)*phi(n/d); d divides n.
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12
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1, 2, 4, 5, 8, 8, 12, 12, 16, 16, 20, 20, 24, 24, 32, 28, 32, 32, 36, 40, 48, 40, 44, 48, 56, 48, 60, 60, 56, 64, 60, 64, 80, 64, 96, 80, 72, 72, 96, 96, 80, 96, 84, 100, 128, 88, 92, 112, 120, 112, 128, 120, 104, 120
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Sum_{d|n} a_d = A018804(n). - Frank Adams-Watters (FrankTAW(AT)Netscape.net), Nov 19 2004
Equals row sums of triangle A159937 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 26 2009]
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FORMULA
| Sum_{k=1..n} phi(gcd(n, k)). Multiplicative with a(p^e) = (e+1)*(p^e - p^(e - 1)) - (e - 1)*(p^(e - 1) - p^(e - 2)). - Vladeta Jovovic (vladeta(AT)eunet.rs), Oct 30 2001
Dirichlet g.f.: zeta(s-1)^2/zeta(s)^2. - Frank Adams-Watters (FrankTAW(AT)Netscape.net), Nov 19 2004
Equals A051731 (inverse Mobius transform) of A018804: (1, 3, 5, 8, 9, 15, 13,...); and row sums of triangle A143258. [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Aug 02 2008]
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MAPLE
| with(numtheory): A029935 := proc(n) local i, j; j := 0; for i in divisors(n) do j := j+phi(i)*phi(n/i); od; j; end;
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MATHEMATICA
| A029935[n_]:=DivisorSum[n, EulerPhi[#]*EulerPhi[n/#]&]; Array[A029935, 50]
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CROSSREFS
| Cf. A029936.
Cf. A159937 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 26 2009]
Sequence in context: A036694 A085624 A061884 * A123291 A099402 A117070
Adjacent sequences: A029932 A029933 A029934 * A029936 A029937 A029938
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KEYWORD
| mult,nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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