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1, 3, 8, 6, 24, 24, 48, 12, 24, 72, 120, 48, 168, 144, 192, 24, 288, 72, 360, 144, 384, 360, 528, 96, 120, 504, 72, 288, 840, 576, 960, 48, 960, 864, 1152, 144, 1368, 1080, 1344, 288, 1680, 1152, 1848, 720, 576, 1584, 2208, 192, 336, 360, 2304, 1008, 2808, 216, 2880, 576, 2880, 2520, 3480, 1152, 3720, 2880, 1152, 96
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OFFSET
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1,2
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LINKS
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FORMULA
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Multiplicative with a(p^e) = (p^2 - 1) * p^(e-1).
Sum_{k=1..n} a(k) ~ c * n^3, where c = 2/Pi^2 = 0.202642... (A185197).
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MATHEMATICA
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f[p_, e_] := (p^2 - 1)*p^(e - 1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 16 2022 *)
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PROG
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(PARI) A345052(n) = { my(f=factor(n)); prod(i=1, #f~, ((f[i, 1]^2)-1)*(f[i, 1]^(f[i, 2]-1))); };
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CROSSREFS
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KEYWORD
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nonn,mult,easy
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AUTHOR
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STATUS
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approved
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