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Greatest common divisor of A003415 (arithmetic derivative) and sigma, the sum of divisors function.
1

%I #8 May 08 2022 10:34:35

%S 1,1,1,1,1,1,1,3,1,1,1,4,1,3,8,1,1,3,1,6,2,1,1,4,1,3,1,8,1,1,1,1,2,1,

%T 12,1,1,3,8,2,1,1,1,12,39,1,1,4,1,3,4,14,1,3,8,4,2,1,1,4,1,3,1,1,6,1,

%U 1,18,2,1,1,39,1,3,1,20,6,1,1,2,1,1,1,4,2,3,8,20,1,3,4,24,2,1,24,4,1,1,3,7,1,1,1,2,1

%N Greatest common divisor of A003415 (arithmetic derivative) and sigma, the sum of divisors function.

%H Antti Karttunen, <a href="/A348028/b348028.txt">Table of n, a(n) for n = 1..65537</a>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

%F a(n) = gcd(A000203(n), A003415(n)).

%o (PARI)

%o A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));

%o A348028(n) = gcd(sigma(n), A003415(n));

%Y Cf. A000203, A003415.

%Y Cf. also A342413, A342458, A343226.

%K nonn

%O 1,8

%A _Antti Karttunen_, Sep 25 2021