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A062949
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Multiplicative with a(p^e) = ((e+1)*p^(e+1)-(e+2)*p^e+1)/(p-1).
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11
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1, 3, 5, 9, 9, 15, 13, 25, 23, 27, 21, 45, 25, 39, 45, 65, 33, 69, 37, 81, 65, 63, 45, 125, 69, 75, 95, 117, 57, 135, 61, 161, 105, 99, 117, 207, 73, 111, 125, 225, 81, 195, 85, 189, 207, 135, 93, 325, 139, 207, 165, 225, 105, 285, 189, 325, 185, 171, 117, 405
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OFFSET
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1,2
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COMMENTS
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Inverse Mobius transform of A062355.
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LINKS
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FORMULA
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a(n) = Sum_{d|n} phi(d)*tau(d).
a(n) = Sum_{k=1..n} tau(n/gcd(n, k)).
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MAPLE
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A062949 := proc(n) add(numtheory[phi](d)*numtheory[tau](d), d=numtheory[divisors](n)) ; end proc: # R. J. Mathar, Feb 09 2011
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MATHEMATICA
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f[p_, e_] := ((e+1)*p^(e+1)-(e+2)*p^e+1)/(p-1); a[1] = 1; a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 60] (* Amiram Eldar, Jul 31 2019 *)
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CROSSREFS
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KEYWORD
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nonn,easy,mult
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AUTHOR
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STATUS
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approved
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