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A160894
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a(n) = ((2^b-1)/phi(n))*Sum_{d|n} Moebius(n/d)*d^(b-1) for b = 5.
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1
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31, 465, 1240, 3720, 4836, 18600, 12400, 29760, 33480, 72540, 45384, 148800, 73780, 186000, 193440, 238080, 161820, 502200, 224440, 580320, 496000, 680760, 394320, 1190400, 604500, 1106700, 903960, 1488000, 783060, 2901600, 954304, 1904640, 1815360, 2427300
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OFFSET
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1,1
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LINKS
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FORMULA
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Sum_{k=1..n} a(k) ~ c * n^4, where c = (31/4) * Product_{p prime} (1 + 1/p^2 + 1/p^3 + 1/p^4) = 14.3522727306... .
Sum_{k>=1} 1/a(k) = (zeta(3)*zeta(4)/31) * Product_{p prime} (1 - 2/p^4 + 1/p^7) = 0.03599754726... . (End)
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MATHEMATICA
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f[p_, e_] := p^(3 e - 3)*(1 + p + p^2 + p^3); a[1] = 31; a[n_] := 31 * Times @@ f @@@ FactorInteger[n]; Array[a, 32] (* Amiram Eldar, Nov 08 2022 *)
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PROG
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(PARI) a(n) = {my(f = factor(n)); 31 * prod(i = 1, #f~, (f[i, 1]^3 + f[i, 1]^2 + f[i, 1] + 1)*f[i, 1]^(3*f[i, 2] - 3)); } \\ Amiram Eldar, Nov 08 2022
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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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