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A335915 Fully multiplicative with a(2) = 1, and a(p) = A000265(p-1)*A000265(p+1) = A000265(p^2 - 1), for odd primes p.

%I A335915 #17 Jan 31 2021 08:11:50
%S A335915 1,1,1,1,3,1,3,1,1,3,15,1,21,3,3,1,9,1,45,3,3,15,33,1,9,21,1,3,105,3,
%T A335915 15,1,15,9,9,1,171,45,21,3,105,3,231,15,3,33,69,1,9,9,9,21,351,1,45,3,
%U A335915 45,105,435,3,465,15,3,1,63,15,561,9,33,9,315,1,333,171,9,45,45,21,195,3,1,105,861,3,27,231,105,15,495,3,63,33,15,69
%N A335915 Fully multiplicative with a(2) = 1, and a(p) = A000265(p-1)*A000265(p+1) = A000265(p^2 - 1), for odd primes p.
%C A335915 For all i, j: A324400(i) = A324400(j) => a(i) = a(j) => A336118(i) = A336118(j).
%H A335915 Antti Karttunen, <a href="/A335915/b335915.txt">Table of n, a(n) for n = 1..8192</a>
%H A335915 Antti Karttunen, <a href="/A335915/a335915.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%F A335915 Completely multiplicative with a(2) = 1, and for odd primes p, a(p) = A000265(p-1)*A000265(p+1).
%F A335915 For all n >= 1, A335904(a(n)) = A336118(n).
%F A335915 For all n >= 0, a(2^n) = a(3^n) = 1, a(5^n) = a(7^n) = 3^n.
%F A335915 a(n) = A336466(n) * A336467(n). - _Antti Karttunen_, Jan 31 2021
%o A335915 (PARI)
%o A335915 A000265(n) = (n>>valuation(n,2));
%o A335915 A335915(n) = { my(f=factor(n)); prod(k=1,#f~,if(2==f[k,1],1,(A000265(f[k,1]-1)*A000265(f[k,1]+1))^f[k,2])); };
%Y A335915 Cf. A000265.
%Y A335915 Cf. also A167344, A324400, A335904, A336118, A336455, A336456, A336466, A336467.
%K A335915 nonn,mult,look
%O A335915 1,5
%A A335915 _Antti Karttunen_, Jul 09 2020