A319356 a(n) = Product_{d|n, d<n} prime(1+A003415(d)), where A003415(d) gives arithmetic derivative of d.

1, 2, 2, 6, 2, 18, 2, 66, 6, 18, 2, 2574, 2, 18, 18, 2706, 2, 3978, 2, 3762, 18, 18, 2, 6226506, 6, 18, 102, 5742, 2, 306774, 2, 370722, 18, 18, 18, 203956038, 2, 18, 18, 14961474, 2, 631098, 2, 8514, 7038, 18, 2, 168047170434, 6, 10602, 18, 10494, 2, 33626034, 18, 32252814, 18, 18, 2, 2529917014482, 2, 18, 9486, 155332518, 18, 1418742, 2, 14058, 18, 1219914, 2

Offset

1,2

Links

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

Formula

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

For all n >= 1:

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

A056239(A064989(a(n)) = A319683(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
A319356(n) = { my(m=1); fordiv(n, d, if(d<n, m *= prime(1+A003415(d)))); (m); };

Crossrefs

Cf. A003415, A319357 (rgs-transform).

Sequence in context: A211776 A325248 A036655 * A098792 A061057 A038667

Adjacent sequences: A319353 A319354 A319355 * A319357 A319358 A319359

Keyword

nonn

Author

Antti Karttunen, Oct 02 2018

Status

approved