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A194532 Jordan function ratio J_6(n)/J_2(n). 1
1, 21, 91, 336, 651, 1911, 2451, 5376, 7371, 13671, 14763, 30576, 28731, 51471, 59241, 86016, 83811, 154791, 130683, 218736, 223041, 310023, 280371, 489216, 406875, 603351, 597051, 823536, 708123, 1244061, 924483, 1376256, 1343433, 1760031, 1595601, 2476656, 1875531, 2744343 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Multiplicative with a(p^e) = p^(4*(e-1))*(p^2+p+1)*(p^2-p+1), e>0.

Dirichlet convolution of A000583 with the multiplicative function which starts 1, 5, 10, 0, 26, 50, 50, 0, 0, 130, 122, 0, 170, 250, 260, 0, 290,..

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = A069091(n)/A007434(n).

Dirichlet generating function zeta(s-4)*product_{primes p} (1+p^(2-s)+p^(-s)).

MAPLE

f:= proc(n) local t;

     mul(t[1]^(4*(t[2]-1))*((t[1]^2+1)^2-t[1]^2), t=ifactors(n)[2])

end proc:

map(f, [$1..100]); # Robert Israel, Jun 14 2016

MATHEMATICA

JordanTotient[n_, k_: 1] := DivisorSum[n, #^k MoebiusMu[n/#] &] /; (n > 0) && IntegerQ@ n; Table[JordanTotient[n, 6]/JordanTotient[n, 2], {n, 12}] (* Michael De Vlieger, Jun 14 2016, after Enrique Pérez Herrero at A065959 *)

CROSSREFS

Cf. A065959.

Sequence in context: A225705 A259758 A203173 * A065827 A143843 A119109

Adjacent sequences:  A194529 A194530 A194531 * A194533 A194534 A194535

KEYWORD

nonn,mult,easy

AUTHOR

R. J. Mathar, Aug 28 2011

STATUS

approved

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Last modified July 29 17:34 EDT 2016. Contains 275165 sequences.