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A336459 a(n) = A065330(sigma(sigma(n))), where A065330 is fully multiplicative with a(2) = a(3) = 1, and a(p) = p for primes p > 3.

%I A336459 #9 Jul 26 2020 09:51:02
%S A336459 1,1,7,1,1,7,5,1,7,13,7,7,1,5,5,1,13,7,7,1,7,91,5,7,1,1,5,5,1,65,7,13,
%T A336459 31,5,31,7,5,7,5,13,1,7,7,7,7,65,31,7,5,1,65,19,5,5,65,5,31,13,7,5,1,
%U A336459 7,35,1,7,403,7,13,7,403,65,7,19,5,7,7,7,5,31,1,133,13,7,7,35,7,5,91,13,91,31,5,85,403
%N A336459 a(n) = A065330(sigma(sigma(n))), where A065330 is fully multiplicative with a(2) = a(3) = 1, and a(p) = p for primes p > 3.
%C A336459 Sequence removes prime factors 2 and 3 from the prime factorization A051027(n) = sigma(sigma(n)).
%C A336459 Like A051027, neither this is multiplicative. For example, we have a(3) = 7, a(7) = 5, but a(21) = 7 <> 35. However, for example, a(10) = 13, and a(3*10) = a(3)*a(10) = 65.
%H A336459 Antti Karttunen, <a href="/A336459/b336459.txt">Table of n, a(n) for n = 1..10000</a>
%H A336459 Antti Karttunen, <a href="/A336459/a336459.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%H A336459 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A336459 a(n) = A336457(A000203(n)) = A065330(A051027(n)).
%o A336459 (PARI)
%o A336459 A065330(n) = (n>>valuation(n, 2)/3^valuation(n, 3));
%o A336459 A336459(n) = A065330(sigma(sigma(n)));
%Y A336459 Cf. A000203, A051027, A065330, A336456 (similar sequence), A336457.
%Y A336459 Cf. also A336561 (positions where this appears to be multiplicative but A051027 does not).
%K A336459 nonn
%O A336459 1,3
%A A336459 _Antti Karttunen_, Jul 25 2020