A381043 Centered pentagonal numbers which are squarefree semiprimes.

6, 51, 106, 141, 226, 391, 526, 681, 766, 951, 1501, 1891, 2031, 2326, 2481, 2641, 3151, 3901, 4101, 4306, 6631, 6891, 7981, 8266, 8851, 10081, 10401, 11391, 13141, 14631, 15406, 16201, 20931, 23281, 24751, 27301, 27826, 28891, 29431, 30526, 32206, 33351, 35701, 36301, 38131, 38751, 41926

Offset: 1

Author

Massimo Kofler, Apr 14 2025

Keywords

• nonn

Comments

Numbers such as 22801=151^2 and 1666681=1291^2 are in A382132 but not here.

Examples

			A005891(1) = 6 = (5*1^2 + 5*1 + 2)/2 = 2*3.
A005891(4) = 51 = (5*4^2 + 5*4 + 2)/2 = 3*17.
A005891(6) = 106 = (5*6^2 + 5*6 + 2)/2 = 2*53.
		

Crossrefs

Intersection of A006881 and A005891.

Cf. A145838, A382132, A364610.

Programs

Mathematica

Select[Table[5*n*(n + 1)/2 + 1, {n, 0, 150}], FactorInteger[#][[;; , 2]] == {1, 1} &] (* Amiram Eldar, Apr 14 2025 *)