cp's OEIS Frontend

A336456 a(n) = A335915(sigma(sigma(n))), where A335915 is a fully multiplicative sequence with a(2) = 1 and a(p) = A000265(p^2 - 1) for odd primes p, with A000265(k) giving the odd part of k.

%I A336456 #7 Jul 24 2020 10:58:13
%S A336456 1,1,3,1,1,3,3,1,3,21,3,3,1,3,3,1,21,3,3,1,3,63,3,3,1,1,3,3,1,63,3,21,
%T A336456 15,3,15,3,3,3,3,21,1,3,3,3,3,63,15,3,3,1,63,45,3,3,63,3,15,21,3,3,1,
%U A336456 3,9,1,3,315,3,21,3,315,63,3,45,3,3,3,3,3,15,1,135,21,3,3,9,3,3,63,21,63,15,3,27,315
%N A336456 a(n) = A335915(sigma(sigma(n))), where A335915 is a fully multiplicative sequence with a(2) = 1 and a(p) = A000265(p^2 - 1) for odd primes p, with A000265(k) giving the odd part of k.
%C A336456 Like A051027, neither this is multiplicative. For example, we have a(3) = 3, a(7) = 3, but a(21) = 3 <> 9. However, for example, a(10) = 21, and a(3*10) = 63.
%H A336456 Antti Karttunen, <a href="/A336456/b336456.txt">Table of n, a(n) for n = 1..10000</a>
%H A336456 Antti Karttunen, <a href="/A336456/a336456.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%F A336456 a(n) = A335915(A000203(A000203(n))) = A336455(A000203(n)) = A335915(A051027(n)).
%o A336456 (PARI)
%o A336456 A000265(n) = (n>>valuation(n,2));
%o A336456 A335915(n) = { my(f=factor(n)); prod(k=1,#f~,if(2==f[k,1],1,(A000265((f[k,1]^2)-1)^f[k,2]))); };
%o A336456 A336456(n) = A335915(sigma(sigma(n)));
%Y A336456 Cf. A000203, A051027, A335915.
%Y A336456 Cf. also A336462, A336463, A336464.
%K A336456 nonn
%O A336456 1,3
%A A336456 _Antti Karttunen_, Jul 22 2020