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

1,2

Links

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

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).

Prog

(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); };

Crossrefs

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

Sequence in context: A368957 A057648 A282460 * A068511 A306544 A060590

Adjacent sequences: A327927 A327928 A327929 * A327931 A327932 A327933

Keyword

nonn

Author

Antti Karttunen, Sep 30 2019

Status

approved