JORDAN's FUNCTION
\[J_{k}(n)\]
\[J_{k}(n)=n^{k}~\prod_{p|n}^{ }(1-\frac{1}{p^{k}})\]
#Jordan's function
def jordan(k, n) :
j = n^k * prod([1 - 1/p^k for p in prime_divisors(n)])
return j
jordan(2, 25)
[jordan(2, n) for n in [1..10]]
\[J_{1}(n)=n^{1}~\prod_{p|n}^{ }(1-\frac{1}{p^{1}})=\varphi (n)\]
A067858 Jordan function J_n(n)
1,3,26,240,3124,45864,823542,16711680,387400806,9990233352,285311670610
A007434 Jordan function J_2(n)
1,3,8,12,24,24,48,48,72,72,120,96,168,144,192,192,288,216,360,288
A059376 Jordan function J_3(n)
1,7,26,56,124,182,342,448,702,868,1330,1456,2196,2394,3224,3584,4912
A059377 Jordan function J_4(n)
1,15,80,240,624,1200,2400,3840,6480,9360,14640,19200,28560,36000,49920
A059378 Jordan function J_5(n)
1,31,242,992,3124,7502,16806,31744,58806,96844,161050,240064,371292,520986