cp's OEIS Frontend

A129514 a(n) = gcd(Sum_{k|n} k, Sum_{1 k does not divide n} k) = gcd(sigma(n), n(n+1)/2 - sigma(n)) = gcd(sigma(n), n(n+1)/2), where sigma(n) = A000203(n).

%I A129514 #24 Jun 28 2025 17:54:27
%S A129514 1,3,2,1,3,3,4,3,1,1,6,2,7,3,24,1,9,3,10,42,1,1,12,60,1,3,2,14,15,3,
%T A129514 16,3,3,1,6,1,19,3,4,10,21,3,22,6,3,1,24,4,1,3,6,2,27,15,4,12,1,1,30,
%U A129514 6,31,3,8,1,3,3,34,6,3,1,36,3,37,3,2,14,3,3,40,6
%N A129514 a(n) = gcd(Sum_{k|n} k, Sum_{1<k<n, k does not divide n} k) = gcd(sigma(n), n(n+1)/2 - sigma(n)) = gcd(sigma(n), n(n+1)/2), where sigma(n) = A000203(n).
%C A129514 a(n) = 1 for n from A260963; a(p) = (p+1)/2 for p prime number >= 3. - _Ctibor O. Zizka_, Nov 27 2021
%F A129514 a(n) = gcd(A000203(n), A000217(n)). - _Ctibor O. Zizka_, Nov 27 2021
%p A129514 A129514 := proc(n) gcd( numtheory[sigma](n),n*(n+1)/2) ; end: seq(A129514(n),n=1..80) ; # _R. J. Mathar_, Oct 30 2007
%t A129514 nterms=100;Table[GCD[DivisorSigma[1,n],PolygonalNumber[n]],{n, nterms}] (* _Paolo Xausa_, Nov 27 2021 *)
%Y A129514 Cf. A000203, A024816.
%K A129514 nonn
%O A129514 1,2
%A A129514 _Leroy Quet_, May 29 2007
%E A129514 More terms from _R. J. Mathar_, Oct 30 2007