A380101 Numbers k such that omega(k-th triangular number) = 2, where omega = A001221.

3, 4, 5, 6, 7, 8, 9, 10, 13, 16, 17, 18, 22, 25, 26, 31, 37, 46, 49, 53, 58, 61, 73, 81, 82, 97, 106, 121, 127, 157, 162, 166, 178, 193, 226, 241, 242, 250, 256, 262, 277, 313, 337, 346, 358, 361, 382, 397, 421, 457, 466, 478, 486, 502, 541, 562, 577, 586, 613

Offset: 1

Author

Juri-Stepan Gerasimov, Jan 12 2025

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Supersequence of A077065 and of A178490.

Cf. A000217, A001221, A119663.

Programs

Magma

[k: k in [1..400] | #PrimeDivisors(k*(k+1) div 2) eq 2];

Maple

filter:= proc(n) local W1, n1, W2; uses numtheory;
     if n::odd then nops(factorset(n)) = 1 and nops(factorset((n+1)/2)) = 1
     else nops(factorset(n/2)) = 1 and nops(factorset(n+1)) = 1
     fi
end proc:
select(filter, [$1..1000]); # Robert Israel, Mar 12 2025

Mathematica

Select[Range[600], PrimeNu[#*(#+1)/2] == 2 &] (* Amiram Eldar, Jan 12 2025 *)

PARI

isok(k) = omega(k*(k+1)/2) == 2; \\ Michel Marcus, Jan 14 2025