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A344697 a(n) = A001615(n) / gcd(sigma(n), A001615(n)).

%I A344697 #15 May 29 2021 20:01:21
%S A344697 1,1,1,6,1,1,1,4,12,1,1,6,1,1,1,24,1,12,1,6,1,1,1,4,30,1,9,6,1,1,1,16,
%T A344697 1,1,1,72,1,1,1,4,1,1,1,6,12,1,1,24,56,30,1,6,1,9,1,4,1,1,1,6,1,1,12,
%U A344697 96,1,1,1,6,1,1,1,48,1,1,30,6,1,1,1,24,108,1,1,6,1,1,1,4,1,12,1,6,1,1,1,16,1,56,12,180
%N A344697 a(n) = A001615(n) / gcd(sigma(n), A001615(n)).
%C A344697 This is not multiplicative. The first point where a(m*n) = a(m)*a(n) does not hold for coprime m and n is 108 = 4*27, where a(108) = 27, although a(4) = 6 and a(27) = 9. See A344702.
%H A344697 Antti Karttunen, <a href="/A344697/b344697.txt">Table of n, a(n) for n = 1..10404</a>
%H A344697 Antti Karttunen, <a href="/A344697/a344697.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%H A344697 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A344697 a(n) = A001615(n) / A344695(n).
%o A344697 (PARI)
%o A344697 A001615(n) = if(1==n,n, my(f=factor(n)); prod(i=1, #f~, f[i, 1]^f[i, 2] + f[i, 1]^(f[i, 2]-1))); \\ After code in A001615
%o A344697 A344697(n) = { my(u=A001615(n)); (u/gcd(u,sigma(n))); };
%Y A344697 Cf. A000203, A001615, A005117, A344695, A344696, A344699, A344702.
%Y A344697 Cf. also A344757.
%K A344697 nonn
%O A344697 1,4
%A A344697 _Antti Karttunen_, May 26 2021