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A160893
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a(n) = Sum_{d|n} Möbius(n/d)*d^5/phi(n).
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5
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1, 31, 121, 496, 781, 3751, 2801, 7936, 9801, 24211, 16105, 60016, 30941, 86831, 94501, 126976, 88741, 303831, 137561, 387376, 338921, 499255, 292561, 960256, 488125, 959171, 793881, 1389296, 732541, 2929531, 954305, 2031616, 1948705
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OFFSET
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1,2
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COMMENTS
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a(n) is the number of lattices L in Z^5 such that the quotient group Z^5 / L is C_nm x (C_m)^4 (and also (C_nm)^4 x C_m), for every m>=1. - Álvar Ibeas, Oct 30 2015
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LINKS
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FORMULA
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Multiplicative with a(p^e) = p^(4e-4)*(1 + p+ p^2 + p^3 + p^4). - R. J. Mathar, Jul 10 2011
Sum_{k=1..n} a(k) ~ c * n^5, where c = (1/5) * Product_{p prime} (1 + (p^4-1)/((p-1)*p^5)) = 0.3799167034... .
Sum_{k>=1} 1/a(k) = zeta(4)*zeta(5) * Product_{p prime} (1 - 2/p^5 + 1/p^9) = 1.0449010968... . (End)
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MAPLE
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A160893 := proc(n) a := 1 ; for f in ifactors(n)[2] do p := op(1, f) ; e := op(2, f) ; a := a*p^(4*e-4)*(1+p+p^2+p^3+p^4) ; end do; a; end proc: # R. J. Mathar, Jul 10 2011
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MATHEMATICA
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f[p_, e_] := p^(4*e - 4)*(1 + p + p^2 + p^3 + p^4); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 40] (* Amiram Eldar, Nov 08 2022 *)
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PROG
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(PARI) a(n) = sumdiv(n, d, moebius(n/d)*d^5/eulerphi(n)); \\ Michel Marcus, Feb 15 2015
(PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, (f[i, 1]^5 - 1)*f[i, 1]^(4*f[i, 2] - 4)/(f[i, 1] - 1)); } \\ Amiram Eldar, Nov 08 2022
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CROSSREFS
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KEYWORD
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nonn,mult
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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