cp's OEIS Frontend

A336455 a(n) = A335915(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 A336455 #11 Jul 24 2020 10:58:05
%S A336455 1,1,1,3,1,1,1,3,21,1,1,3,3,1,1,15,1,21,3,3,1,1,1,3,15,3,3,3,3,1,1,3,
%T A336455 1,1,1,63,45,3,3,3,3,1,15,3,21,1,1,15,45,15,1,9,1,3,1,3,3,3,3,3,15,1,
%U A336455 21,63,3,1,9,3,1,1,1,63,171,45,15,9,1,3,3,15,225,3,3,3,1,15,3,3,3,21,3,3,1,1,3,3,9,45,21,45
%N A336455 a(n) = A335915(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.
%H A336455 Antti Karttunen, <a href="/A336455/b336455.txt">Table of n, a(n) for n = 1..10000</a>
%H A336455 Antti Karttunen, <a href="/A336455/a336455.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%F A336455 a(n) = A335915(A000203(n)).
%F A336455 Multiplicative with a(p^e) = A335915(1 + p + p^2 + ... + p^e).
%F A336455 a(A000203(n)) = A336456(n).
%o A336455 (PARI)
%o A336455 A000265(n) = (n>>valuation(n,2));
%o A336455 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 A336455 A336455(n) = A335915(sigma(n));
%o A336455 \\ Alternatively, as:
%o A336455 A336455(n) =  { my(f=factor(n)); prod(k=1,#f~,A335915(((f[k,1]^(1+f[k,2]))-1)/(f[k,1]-1))); };
%Y A336455 Cf. A000265, A000203, A335915, A336456.
%Y A336455 Cf. also A336461, A336462, A336464.
%K A336455 nonn,mult
%O A336455 1,4
%A A336455 _Antti Karttunen_, Jul 22 2020