A365849 Triangular numbers that are the product of two distinct prime numbers of the form 4*k + 3.

21, 253, 1081, 13861, 34453, 64261, 73153, 114481, 126253, 258121, 351541, 371953, 392941, 482653, 869221, 933661, 1034641, 1104841, 1660753, 2077741, 2126953, 2434321, 2992681, 4142881, 4212253, 4495501, 4567753, 4862521, 5013361, 6561253, 7459453, 8026021

Offset: 1

Author

Marius A. Burtea, Oct 09 2023

Keywords

• nonn

Comments

Intersection of A068443 and A016105.

Subsequence of A156592.

Apparently, a(n) == 1 (mod 36) for n >= 2. - Hugo Pfoertner, Nov 03 2023

Examples

			21 = A068443(4) and 21 = A016105(1), so 21 is a term.
253 = A068443(7) and 253 = A016105(18), so 253 is a term.
		

Crossrefs

Cf. A000217, A001358, A068443, A156592, A016105.

Programs

Magma

pd:=PrimeDivisors; blum:=func; [n:n in [1..9000000]|IsSquare(8*n+1) and blum(n)];

Mathematica

Select[Accumulate[Range[4500]], (f = FactorInteger[#])[[;; , 2]] == {1, 1} && Mod[f[[;; , 1]], 4] == {3, 3} &] (* Amiram Eldar, Oct 11 2023 *)