A139131 Squarefree kernel of n*(n+1)/2.

1, 3, 6, 10, 15, 21, 14, 6, 15, 55, 66, 78, 91, 105, 30, 34, 51, 57, 190, 210, 231, 253, 138, 30, 65, 39, 42, 406, 435, 465, 62, 66, 561, 595, 210, 222, 703, 741, 390, 410, 861, 903, 946, 330, 345, 1081, 282, 42, 35, 255, 1326, 1378, 159, 165, 770, 798, 1653, 1711

Offset: 1

Author

Reinhard Zumkeller, Apr 10 2008

Keywords

• nonn
• easy

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000217, A007947, A014601, A014695, A078636.

Programs

Mathematica

Times@@(Transpose[FactorInteger[#]][[1]])&/@Accumulate[Range[60]] (* Harvey P. Dale, Jun 06 2013 *)

PARI

a(n) = vecprod(factor(n*(n+1)/2)[, 1]); \\ Amiram Eldar, May 12 2025

Formula

a(n) = A007947(A000217(n)).

a(A014601(n)) = A078636(A014601(n)).

a(n) = A078636(n) / A014695(n).