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A329043 a(n) = Product_{d|A122111(n), d>1} A008578(1+A286561(n,d)), where A286561(n,d) gives the exponent of the highest power of d dividing n.

%I A329043 #6 Nov 08 2019 18:15:10
%S A329043 1,2,1,1,1,8,1,1,6,2,1,3,1,2,2,1,1,3,1,48,2,2,1,5,1,2,1,6,1,128,1,1,2,
%T A329043 2,1,3,1,2,2,10,1,8,1,6,2,2,1,7,1,3,2,6,1,1,1,320,2,2,1,12,1,2,1,1,1,
%U A329043 8,1,6,2,8,1,3,1,2,48,6,1,8,1,21,1,2,1,3072,1,2,2,20,1,8,1,6,2,2,1,11,1,1,1,1,1,8,1,20,8
%N A329043 a(n) = Product_{d|A122111(n), d>1} A008578(1+A286561(n,d)), where A286561(n,d) gives the exponent of the highest power of d dividing n.
%H A329043 Antti Karttunen, <a href="/A329043/b329043.txt">Table of n, a(n) for n = 1..10000</a>
%H A329043 Antti Karttunen, <a href="/A329043/a329043.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%H A329043 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A329043 a(n) = Product_{d|A122111(n), d>1} A008578(1+A286561(n,d)).
%F A329043 1+A001222(a(n)) = A329036(n).
%o A329043 (PARI)
%o A329043 A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
%o A329043 A122111(n) = if(1==n,n,prime(bigomega(n))*A122111(A064989(n)));
%o A329043 A329043(n) = { my(m=1,v); fordiv(A122111(n),d,if((d>1) && ((v = valuation(n,d))>0), m *= prime(v))); (m); };
%Y A329043 Cf. A001222, A008578, A122111, A286561, A329036, A329042.
%Y A329043 Cf. also A327167.
%K A329043 nonn
%O A329043 1,2
%A A329043 _Antti Karttunen_, Nov 08 2019