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A353420 a(n) = A126760(A003961(n)).

%I A353420 #12 Apr 20 2022 22:48:35
%S A353420 1,1,2,1,3,2,4,1,9,3,5,2,6,4,12,1,7,9,8,3,19,5,10,2,17,6,42,4,11,12,
%T A353420 13,1,22,7,26,9,14,8,29,3,15,19,16,5,59,10,18,2,41,17,32,6,20,42,31,4,
%U A353420 39,11,21,12,23,13,92,1,40,22,24,7,49,26,25,9,27,14,82,8,48,29,28,3,209,15,30,19,45,16,52,5,33
%N A353420 a(n) = A126760(A003961(n)).
%H A353420 Antti Karttunen, <a href="/A353420/b353420.txt">Table of n, a(n) for n = 1..16384</a>
%H A353420 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A353420 a(n) = A126760(A003961(n)) = A249746(A003602(n)) = A126760(A249735(A003602(n))).
%F A353420 a(n) = A353336(4*n) = A353336(n) - A353335(n).
%F A353420 For all n >= 1, a(n) = a(2*n) = a(A000265(n)).
%F A353420 For all n >= 1, A249745(a(n)) = A003602(n).
%o A353420 (PARI)
%o A353420 A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
%o A353420 A126760(n) = {n&&n\=3^valuation(n, 3)<<valuation(n, 2); n%3+n\6*2}; \\ From A126760
%o A353420 A353420(n) = A126760(A003961(n));
%Y A353420 Cf. A000265, A003602, A003961, A048673, A126760, A249735, A249745, A249746.
%Y A353420 Cf. A353335 (Dirichlet inverse), A353336 (sum with it).
%K A353420 nonn
%O A353420 1,3
%A A353420 _Antti Karttunen_, Apr 20 2022