A127991 2*n^3 - 2*n + 9 divided by 3*largest prime factor.

1, 1, 1, 1, 1, 11, 1, 3, 21, 39, 1, 31, 1, 1, 1, 7, 297, 9, 351, 1, 1, 19, 91, 1, 101, 141, 51, 33, 37, 49, 1, 299, 37, 1, 3, 39, 21, 1, 11, 1, 19, 1, 31, 1071, 351, 9, 43, 1, 481, 11, 511, 83, 3, 3, 69, 1, 1, 91, 1, 19, 187, 39, 219, 417, 553, 37, 1, 1, 1, 1369, 117, 693, 423, 31

Offset: 1

Author

Artur Jasinski, Feb 10 2007

Keywords

• nonn
• easy

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A127979, A127990, A127992.

Programs

Mathematica

a = {}; Do[AppendTo[a, 2n^3 - 2n + 9], {n, 1, 300}]; b = {}; Do[c = FactorInteger[a[[n]]]; d = c[[Length[c]]]; AppendTo[b, a[[n]]/(3 d[[1]])], {n, 1, Length[a]}]; b

PARI

gpf(n)=my(f=factor(n)[,1]); if(n==1,1,f[#f]);
a(n)=my(m=2*n^3-2*n+9); m/gpf(m)/3 \\ Charles R Greathouse IV, Mar 13 2020

Formula

a(n) = A127989(n)/(3*A006530(A127989(n))). - Amiram Eldar, Mar 13 2020