A380913 Squarefree semiprimes that are centered triangular numbers.

10, 46, 85, 166, 235, 274, 514, 694, 901, 1135, 1219, 1306, 1585, 1891, 2461, 2839, 3106, 3385, 3826, 3979, 4135, 5311, 5674, 6049, 6835, 7246, 8551, 9481, 10966, 11485, 11749, 12286, 12559, 13969, 15151, 15454, 17335, 18649, 18985, 19666, 21421, 21781, 22879, 23626

Offset: 1

Author

Massimo Kofler, Feb 08 2025

Keywords

• nonn

Comments

4=2^2, 361=19^2, 6241=79^2 are centered triangular numbers but not squarefree.

Examples

			10 = 2 * 5 which is the 3rd centered triangular number.
46 = 2 * 23 which is the 6th centered triangular number.
85 = 5 * 17 which is the 7th centered triangular number.
		

Crossrefs

Intersection of A005448 and A006881.

Cf. A184481, A359624, A359845.

Programs

Mathematica

Select[Table[3*n*(n-1)/2 + 1, {n, 1, 130}], FactorInteger[#][[;; , 2]] == {1, 1} &] (* Amiram Eldar, Feb 08 2025 *)