A353420 - OEIS

%I #12 Apr 20 2022 22:48:35

%S 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 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 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 a(n) = A126760(A003961(n)).

%H Antti Karttunen, <a href="/A353420/b353420.txt">Table of n, a(n) for n = 1..16384</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%F a(n) = A126760(A003961(n)) = A249746(A003602(n)) = A126760(A249735(A003602(n))).

%F a(n) = A353336(4*n) = A353336(n) - A353335(n).

%F For all n >= 1, a(n) = a(2*n) = a(A000265(n)).

%F For all n >= 1, A249745(a(n)) = A003602(n).

%o (PARI)

%o A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };

%o A126760(n) = {n&&n\=3^valuation(n, 3)<<valuation(n, 2); n%3+n\6*2}; \\ From A126760

%o A353420(n) = A126760(A003961(n));

%Y Cf. A000265, A003602, A003961, A048673, A126760, A249735, A249745, A249746.

%Y Cf. A353335 (Dirichlet inverse), A353336 (sum with it).

%K nonn

%O 1,3

%A _Antti Karttunen_, Apr 20 2022