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a(n) = Product_{d|n, d<n} prime(1+A003415(d)), where A003415(d) gives arithmetic derivative of d.
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%I #7 Oct 03 2018 21:35:28

%S 1,2,2,6,2,18,2,66,6,18,2,2574,2,18,18,2706,2,3978,2,3762,18,18,2,

%T 6226506,6,18,102,5742,2,306774,2,370722,18,18,18,203956038,2,18,18,

%U 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

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

%H Antti Karttunen, <a href="/A319356/b319356.txt">Table of n, a(n) for n = 1..8192</a>

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

%F For all n >= 1:

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

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

%o (PARI)

%o 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

%o A319356(n) = { my(m=1); fordiv(n, d, if(d<n, m *= prime(1+A003415(d)))); (m); };

%Y Cf. A003415, A319357 (rgs-transform).

%K nonn

%O 1,2

%A _Antti Karttunen_, Oct 02 2018