A319356 a(n) = Product_{d|n, dA003415(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

Author

Antti Karttunen, Oct 02 2018

Keywords

• nonn

Links

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

Crossrefs

Cf. A003415, A319357 (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
A319356(n) = { my(m=1); fordiv(n, d, if(dA003415(d)))); (m); };

Formula

a(n) = Product_{d|n, dA000040(1+A003415(d)).

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

A056239(A064989(a(n))) = A319683(n).