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A329042 a(n) = Product_{d|n, d>1} A008578(1+A286561(A122111(n),d)), where A286561(x,d) gives the exponent of the highest power of d dividing x.

%I A329042 #7 Nov 08 2019 18:14:58
%S A329042 1,2,1,1,1,8,1,1,6,3,1,2,1,5,3,1,1,2,1,48,3,7,1,2,1,11,1,10,1,128,1,1,
%T A329042 3,13,1,2,1,17,3,6,1,12,1,21,3,19,1,2,1,2,3,33,1,1,1,320,3,23,1,8,1,
%U A329042 29,1,1,1,20,1,65,3,8,1,2,1,31,48,85,1,28,1,6,1,37,1,3072,1,41,3,42,1,8,1,133,3,43,1,2,1,1,1,1,1,44,1,66,12
%N A329042 a(n) = Product_{d|n, d>1} A008578(1+A286561(A122111(n),d)), where A286561(x,d) gives the exponent of the highest power of d dividing x.
%H A329042 Antti Karttunen, <a href="/A329042/b329042.txt">Table of n, a(n) for n = 1..10000</a>
%H A329042 Antti Karttunen, <a href="/A329042/a329042.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%H A329042 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A329042 a(n) = Product_{d|n, d>1} A008578(1+A286561(A122111(n),d)).
%F A329042 1+A001222(a(n)) = A329036(n).
%o A329042 (PARI)
%o A329042 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 A329042 A122111(n) = if(1==n,n,prime(bigomega(n))*A122111(A064989(n)));
%o A329042 A329042(n) = { my(m=1,x=A122111(n),v); fordiv(n,d,if((d>1) && ((v = valuation(x,d))>0), m *= prime(v))); (m); };
%Y A329042 Cf. A001222, A008578, A122111, A286561, A329036, A329043.
%Y A329042 Cf. also A329037.
%K A329042 nonn
%O A329042 1,2
%A A329042 _Antti Karttunen_, Nov 08 2019