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A194533 Jordan function ratio J_8(n)/J_2(n). 0
1, 85, 820, 5440, 16276, 69700, 120100, 348160, 597780, 1383460, 1786324, 4460800, 4855540, 10208500, 13346320, 22282240, 24221380, 50811300, 47176564, 88541440, 98482000, 151837540, 148316260, 285491200, 254312500, 412720900, 435781620, 653344000, 595531444 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
FORMULA
a(n) = A069093(n)/A007434(n) = A065960(n) * A065958(n).
Multiplicative with a(p^e) = p^(6*(e-1))*(p^2+1)*(p^4+1), e>0.
Dirichlet g.f.: zeta(s-6)*Product_{primes p} (1+p^(4-s)+p^(2-s)+p^(-s)).
Dirichlet convolution of A001014 with the multiplicative sequence 1, 21, 91, 0, 651, 1911, 2451, 0, 0, 13671, 14763, 0, 28731, 51471...
Sum_{k=1..n} a(k) ~ c * n^7 / 7, where c = Product_{primes p} (1 + 1/p^3 + 1/p^5 + 1/p^7) = 1.22847463998021088097249049512949441921891884186337179613337753... - Vaclav Kotesovec, Dec 18 2019
MATHEMATICA
f[p_, e_] := p^(6*(e - 1))*(p^2 + 1)*(p^4 + 1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Nov 01 2022 *)
CROSSREFS
Sequence in context: A297599 A173470 A202009 * A069308 A183643 A206163
KEYWORD
nonn,mult,easy
AUTHOR
R. J. Mathar, Aug 28 2011
STATUS
approved

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Last modified May 24 01:38 EDT 2024. Contains 372768 sequences. (Running on oeis4.)