A326069 - OEIS

%I #7 Jun 08 2019 17:53:24

%S 1,1,2,1,4,2,6,1,5,2,10,4,12,2,3,1,16,1,18,2,1,2,22,4,19,2,14,4,28,6,

%T 30,1,3,2,1,1,36,2,1,2,40,2,42,4,3,2,46,4,41,1,3,2,52,2,1,8,1,2,58,12,

%U 60,2,1,1,1,6,66,2,3,2,70,1,72,2,2,4,1,2,78,2,41,2,82,4,1,2,3,4,88,6,7,4,1,2,5,4,96,1,3,1,100,6,102,2,3

%N a(n) = gcd((sigma(n) - sigma(A032742(n))) - n, n - sigma(A032742(n))), where A032742 gives the largest proper divisor of n.

%H Antti Karttunen, <a href="/A326069/b326069.txt">Table of n, a(n) for n = 1..16384</a>

%H Antti Karttunen, <a href="/A326069/a326069.txt">Data supplement: n, a(n) computed for n = 1..65537</a>

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

%F a(n) = gcd(A326067(n), A326068(n)) = gcd(A326066(n) - n, n - A326065(n)).

%o (PARI)

%o A032742(n) = if(1==n,n,n/vecmin(factor(n)[,1]));

%o A326066(n) = (sigma(n) - sigma(A032742(n)));

%o A326067(n) = (A326066(n) - n);

%o A326065(n) = sigma(A032742(n));

%o A326068(n) = (n - A326065(n));

%o A326069(n) = gcd(A326067(n), A326068(n));

%Y Cf. A000203, A032742, A326065, A326066, A326067, A326068.

%Y Cf. also A009194, A325385, A325813, A325975, A326046, A326047, A326048, A326056, A326057, A326060, A326062.

%K nonn

%O 1,3

%A _Antti Karttunen_, Jun 06 2019