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a(n) = gcd(n*d(n), sigma(n)), where d(n) = number of divisors of n (A000005) and sigma(n) = sum of divisors of n (A000203).
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%I #14 Feb 17 2023 15:33:22

%S 1,1,2,1,2,12,2,1,1,2,2,4,2,8,12,1,2,3,2,6,4,4,2,12,1,2,4,56,2,24,2,3,

%T 12,2,4,1,2,4,4,10,2,48,2,12,6,8,2,4,3,3,12,2,2,24,4,8,4,2,2,24,2,8,2,

%U 1,4,48,2,6,12,16,2,3,2,2,2,4,4,24,2,2,1,2,2,112,4,4,12,4,2,18,28,24,4,8,20,36,2,3,6,1,2,24,2,2,24

%N a(n) = gcd(n*d(n), sigma(n)), where d(n) = number of divisors of n (A000005) and sigma(n) = sum of divisors of n (A000203).

%C Records 1, 2, 12, 56, 112, 120, 336, 720, 992, 2016, 4368, 8640, 14880, 16256, 26208, 59520, 78624, 120960, 131040, 191520, 227584, 297600, ... occur at positions: 1, 3, 6, 28, 84, 120, 140, 270, 496, 672, 1638, 2970, 6200, 8128, 8190, 18600, 27846, 30240, 32760, 55860, 105664, 117800, ... . Note that A001599 is not a subsequence of the latter, as at least 18620 (present in A001599) is missing.

%H Antti Karttunen, <a href="/A324121/b324121.txt">Table of n, a(n) for n = 1..10080</a>

%H Antti Karttunen, <a href="/A324121/a324121.txt">Data supplement: n, a(n) computed for n = 1..117800</a>

%F a(n) = gcd(A000203(n), A038040(n)).

%F a(n) = A324058(A156552(n)).

%t Table[GCD[n DivisorSigma[0,n],DivisorSigma[1,n]],{n,120}] (* _Harvey P. Dale_, Feb 17 2023 *)

%o (PARI) A324121(n) = gcd(sigma(n),n*numdiv(n));

%Y Cf. A000005, A000203, A001599, A038040, A106315, A106316, A156552, A324045, A324046, A324047, A324058, A324122.

%K nonn

%O 1,3

%A _Antti Karttunen_, Feb 15 2019