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A161139
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a(n) = Sum_{d|n} Moebius(n/d)*d^(b-1)/phi(n) for b = 16.
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4
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1, 32767, 7174453, 536854528, 7629394531, 235085301451, 791260251657, 8795824586752, 34315186290957, 249992370597277, 417724816941565, 3851637578973184, 4265491084507563, 25927224666044919, 54736732481116543
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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^15 such that the quotient group Z^15 / L is C_n. - Álvar Ibeas, Nov 26 2015
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LINKS
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FORMULA
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a(n) = J_15(n)/J_1(n), where J_15 and J_1(n) = A000010(n) are Jordan functions. - R. J. Mathar, Jul 12 2011
Multiplicative with a(p^e) = p^(14e-14) * (p^15-1) / (p-1).
For squarefree n, a(n) = A000203(n^14). (End)
Sum_{k=1..n} a(k) ~ c * n^15, where c = (1/15) * Product_{p prime} (1 + (p^14-1)/((p-1)*p^15)) = 0.1295704557... .
Sum_{k>=1} 1/a(k) = zeta(14)*zeta(15) * Product_{p prime} (1 - 2/p^15 + 1/p^29) = 1.00003065989236... . (End)
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MAPLE
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add(numtheory[mobius](n/d)*d^15, d=numtheory[divisors](n)) ;
%/numtheory[phi](n) ;
end proc:
for n from 1 to 5000 do
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MATHEMATICA
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f[p_, e_] := p^(14*e - 14) * (p^15-1) / (p-1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 20] (* Amiram Eldar, Nov 08 2022 *)
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PROG
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(PARI) vector(100, n, sumdiv(n^14, d, if(ispower(d, 15), moebius(sqrtnint(d, 15))*sigma(n^14/d), 0))) \\ Altug Alkan, Nov 26 2015
(PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, (f[i, 1]^15 - 1)*f[i, 1]^(14*f[i, 2] - 14)/(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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