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A365849 Triangular numbers that are the product of two distinct prime numbers of the form 4*k + 3. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Intersection of A068443 and A016105.
Subsequence of A156592.
Apparently, a(n) == 1 (mod 36) for n >= 2. - Hugo Pfoertner, Nov 03 2023
LINKS
EXAMPLE
21 = A068443(4) and 21 = A016105(1), so 21 is a term.
253 = A068443(7) and 253 = A016105(18), so 253 is a term.
MATHEMATICA
Select[Accumulate[Range[4500]], (f = FactorInteger[#])[[;; , 2]] == {1, 1} && Mod[f[[;; , 1]], 4] == {3, 3} &] (* Amiram Eldar, Oct 11 2023 *)
PROG
(Magma) pd:=PrimeDivisors; blum:=func<n|#Divisors(n) eq 4 and #pd(n) eq 2 and pd(n)[1] mod 4 eq 3 and pd(n)[2] mod 4 eq 3>; [n:n in [1..9000000]|IsSquare(8*n+1) and blum(n)];
CROSSREFS
Sequence in context: A036220 A022649 A165094 * A360804 A322500 A241632
KEYWORD
nonn
AUTHOR
Marius A. Burtea, Oct 09 2023
STATUS
approved

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Last modified February 24 14:59 EST 2024. Contains 370305 sequences. (Running on oeis4.)