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A322310 a(n) = Product_{d|n, d+1 is prime} A008578(1+[Sum_{i=0..A286561(n,1+d)} A320000((n/d)/((1+d)^i), 1+d)]). Here A286561(n,k) gives the k-valuation of n (for k > 1).

%I A322310 #13 Dec 03 2018 18:29:36
%S A322310 3,6,1,10,1,12,1,14,1,4,1,28,1,1,1,22,1,12,1,20,1,4,1,102,1,1,1,4,1,4,
%T A322310 1,26,1,1,1,66,1,1,1,104,1,12,1,6,1,4,1,92,1,1,1,4,1,4,1,6,1,4,1,132,
%U A322310 1,1,1,34,1,4,1,1,1,4,1,1240,1,1,1,1,1,4,1,57,1,4,1,21,1,1,1,28,1,1,1,6,1,1,1,492,1,1,1,12,1,4,1,6,1
%N A322310 a(n) = Product_{d|n, d+1 is prime} A008578(1+[Sum_{i=0..A286561(n,1+d)} A320000((n/d)/((1+d)^i), 1+d)]). Here A286561(n,k) gives the k-valuation of n (for k > 1).
%H A322310 Antti Karttunen, <a href="/A322310/b322310.txt">Table of n, a(n) for n = 1..16384</a>
%F A322310 a(n) = Product_{d|n} A008578(1+[Sum_{i=0..A286561(n,1+d)} A320000((n/d)/((1+d)^i), 1+d)])^A010051(1+d).
%F A322310 For all n, A056239(a(n)) = A014197(n).
%o A322310 (PARI)
%o A322310 A320000sq(n, k) = if(1==n, if(1==k,2,1), sumdiv(n, d, if(d>=k && isprime(d+1), my(p=d+1, q=n/d); sum(i=0, valuation(n, p), A320000sq(q/(p^i), p))))); \\ From A320000
%o A322310 A322310(n) = if(1==n,3,my(m=1); fordiv(n,d, my(s, p=d+1, q=n/d); if(isprime(p) && (s = sum(i=0,valuation(n, p), A320000sq(q/(p^i),p))), m *= prime(s))); (m));
%Y A322310 Cf. A014197, A320000, A322311 (rgs-transform).
%Y A322310 Cf. also A322312.
%K A322310 nonn
%O A322310 1,1
%A A322310 _Antti Karttunen_, Dec 03 2018