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).

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, 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, 6, 31, 3, 8, 1, 3, 3, 34, 6, 3, 1, 36, 3, 37, 3, 2, 14, 3, 3, 40, 6

Offset

1,2

Comments

a(n) = 1 for n from A260963; a(p) = (p+1)/2 for p prime number >= 3.- Ctibor O. Zizka, November 27 2021

Links

Table of n, a(n) for n=1..80.

Formula

a(n) = gcd(A000203(n), A000217(n)).- Ctibor O. Zizka, November 27 2021

Maple

A129514 := proc(n) gcd( numtheory[sigma](n), n*(n+1)/2) ; end: seq(A129514(n), n=1..80) ; # R. J. Mathar, Oct 30 2007

Mathematica

nterms=100; Table[GCD[DivisorSigma[1, n], PolygonalNumber[n]], {n, nterms}] (* Paolo Xausa, Nov 27 2021 *)

Crossrefs

Cf. A000203, A024816.

Sequence in context: A230493 A128262 A140414 * A175506 A211705 A010267

Adjacent sequences: A129511 A129512 A129513 * A129515 A129516 A129517

Keyword

nonn

Author

Leroy Quet, May 29 2007

Extensions

More terms from R. J. Mathar, Oct 30 2007

Status

approved