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

1,1

Comments

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

Links

Table of n, a(n) for n=1..44.

Example

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.

Mathematica

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

Crossrefs

Intersection of A005448 and A006881.

Cf. A184481, A359624, A359845.

Sequence in context: A279092 A007941 A007940 * A082604 A281550 A248575

Adjacent sequences: A380910 A380911 A380912 * A380914 A380915 A380916

Keyword

nonn,new

Author

Massimo Kofler, Feb 08 2025

Status

approved