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A160895
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a(n) = Sum_{d|n} Moebius(n/d)*d^(b-1)/phi(n) for b = 7.
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5
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1, 63, 364, 2016, 3906, 22932, 19608, 64512, 88452, 246078, 177156, 733824, 402234, 1235304, 1421784, 2064384, 1508598, 5572476, 2613660, 7874496, 7137312, 11160828, 6728904, 23482368, 12206250, 25340742, 21493836, 39529728, 21243690, 89572392
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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^6 such that the quotient group Z^6 / L is C_nm x (C_m)^5 (and also (C_nm)^5 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^(5e-5)*(1+p+p^2+p^3+p^4+p^5). - R. J. Mathar, Jul 10 2011
Sum_{k=1..n} a(k) ~ c * n^6, where c = (1/6) * Product_{p prime} (1 + (p^5-1)/((p-1)*p^6)) = 0.3203646372... .
Sum_{k>=1} 1/a(k) = zeta(5)*zeta(6) * Product_{p prime} (1 - 2/p^6 + 1/p^11) = 1.0195114923... . (End)
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MAPLE
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A160895 := proc(n) a := 1 ; for f in ifactors(n)[2] do p := op(1, f) ; e := op(2, f) ; a := a*p^(5*e-5)*(1+p+p^2+p^3+p^4+p^5) ; end do; a; end proc: # R. J. Mathar, Jul 10 2011
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MATHEMATICA
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f[p_, e_] := p^(5*e - 5) * (p^6-1) / (p-1); ; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 30] (* Amiram Eldar, Nov 08 2022 *)
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PROG
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(PARI) vector(50, n, sumdiv(n^5, d, if(ispower(d, 6), moebius(sqrtnint(d, 6))*sigma(n^5/d), 0))) \\ Altug Alkan, Oct 30 2014
(PARI) a(n) = {f = factor(n); for (i=1, #f~, p = f[i, 1]; f[i, 1] = p^(5*f[i, 2]-5)*(1+p+p^2+p^3+p^4+p^5); f[i, 2] = 1; ); factorback(f); } \\ Michel Marcus, Nov 12 2015
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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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