A327930 Product_{d|n, d>1} prime(A003415(d)), where A003415(x) gives the arithmetic derivative of x.

1, 2, 2, 14, 2, 44, 2, 518, 26, 68, 2, 16324, 2, 92, 76, 67858, 2, 41756, 2, 42364, 116, 164, 2, 116569684, 58, 188, 2678, 84364, 2, 3609848, 2, 27753922, 172, 268, 148, 4353104756, 2, 292, 212, 528236716, 2, 10506584, 2, 256004, 164996, 388, 2, 9360895334252, 86, 388484, 284, 346108, 2, 1802063692, 212, 1495183172, 316

Offset: 1

Author

Antti Karttunen, Sep 30 2019

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..8192

Crossrefs

Cf. A000040, A001221, A001222, A003415, A007814, A056239, A064989, A319356, A319684, A319685, A327931 (rgs-transform).

Programs

PARI

A003415(n) = {my(fac); if(n<1, 0, fac=factor(n); sum(i=1, matsize(fac)[1], n*fac[i, 2]/fac[i, 1]))}; \\ From A003415
A327930(n) = { my(m=1); fordiv(n,d,if((d>1), m *= prime(A003415(d)))); (m); };

Formula

a(n) = Product_{d|n, d>1} A000040(A003415(d)).

For all n >= 2, a(n) = prime(A003415(n)) * A064989(A319356(n)).

A001221(a(n)) = A319685(n).

A001222(a(n)) = A032741(n).

A007814(a(n)) = A001221(n).

A056239(a(n)) = A319684(n).