A172253 Numbers k such that the squarefree kernel of 9^k*(9^k - 1) is 3*(9^k - 1)/4.

1, 3, 7, 9, 11, 13, 17, 19, 23, 27, 29, 31, 33, 37, 41, 43, 47, 49, 51, 53, 57, 59, 61, 67, 69, 71, 73, 77, 79, 81, 83, 87, 89, 91, 93, 97, 99, 101, 103, 107, 109, 111, 113, 119, 121, 123, 127, 129, 131, 133, 137, 139, 141, 143, 149, 151, 153, 157, 159, 161

Offset: 1

Author

Artur Jasinski, Jan 29 2010

Keywords

• nonn
• hard

Comments

From Artur Jasinski: (Start)

The maximal value of the squarefree kernel of a*b*9^k for every number 9^k and every a,b such that a + b = 9^k and gcd(a,b,3)=1 is never less than 3*(9^k - 1)/4 and is exactly equal to 3*(9^k - 1)/4 for exponents k in this sequence.

Conjecture: This sequence is infinite. (End)

Crossrefs

Cf. A007947, A054880

Programs

PARI

rad(n) = factorback(factor(n)[, 1]); \\ A007947
isok(k) = rad(9^k*(9^k - 1)) == 3*(9^k - 1)/4; \\ Michel Marcus, Dec 24 2022

Extensions

Edited by Jon E. Schoenfield, Dec 23 2022

More terms from Sean A. Irvine, Jun 15 2024