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A344696 a(n) = sigma(n) / gcd(sigma(n), A001615(n)).

%I A344696 #15 May 29 2021 20:01:10
%S A344696 1,1,1,7,1,1,1,5,13,1,1,7,1,1,1,31,1,13,1,7,1,1,1,5,31,1,10,7,1,1,1,
%T A344696 21,1,1,1,91,1,1,1,5,1,1,1,7,13,1,1,31,57,31,1,7,1,10,1,5,1,1,1,7,1,1,
%U A344696 13,127,1,1,1,7,1,1,1,65,1,1,31,7,1,1,1,31,121,1,1,7,1,1,1,5,1,13,1,7,1,1,1,21,1,57,13
%N A344696 a(n) = sigma(n) / gcd(sigma(n), A001615(n)).
%C A344696 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) = 35, although a(4) = 7 and a(27) = 10. See A344702.
%H A344696 Antti Karttunen, <a href="/A344696/b344696.txt">Table of n, a(n) for n = 1..10404</a>
%H A344696 Antti Karttunen, <a href="/A344696/a344696.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%H A344696 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A344696 a(n) = A000203(n) / A344695(n).
%o A344696 (PARI)
%o A344696 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 A344696 A344696(n) = { my(u=sigma(n)); (u/gcd(u,A001615(n))); };
%Y A344696 Cf. A000203, A001615, A005117 (positions of ones), A344695, A344697, A344698, A344702.
%Y A344696 Cf. also A344756.
%K A344696 nonn
%O A344696 1,4
%A A344696 _Antti Karttunen_, May 26 2021