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

%I A380101 #22 Mar 13 2025 02:54:42
%S A380101 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,
%T A380101 97,106,121,127,157,162,166,178,193,226,241,242,250,256,262,277,313,
%U A380101 337,346,358,361,382,397,421,457,466,478,486,502,541,562,577,586,613
%N A380101 Numbers k such that omega(k-th triangular number) = 2, where omega = A001221.
%H A380101 Robert Israel, <a href="/A380101/b380101.txt">Table of n, a(n) for n = 1..10000</a>
%p A380101 filter:= proc(n) local W1, n1, W2; uses numtheory;
%p A380101      if n::odd then nops(factorset(n)) = 1 and nops(factorset((n+1)/2)) = 1
%p A380101      else nops(factorset(n/2)) = 1 and nops(factorset(n+1)) = 1
%p A380101      fi
%p A380101 end proc:
%p A380101 select(filter, [$1..1000]); # _Robert Israel_, Mar 12 2025
%t A380101 Select[Range[600], PrimeNu[#*(#+1)/2] == 2 &] (* _Amiram Eldar_, Jan 12 2025 *)
%o A380101 (Magma) [k: k in [1..400] | #PrimeDivisors(k*(k+1) div 2) eq 2];
%o A380101 (PARI) isok(k) = omega(k*(k+1)/2) == 2; \\ _Michel Marcus_, Jan 14 2025
%Y A380101 Supersequence of A077065 and of A178490.
%Y A380101 Cf. A000217, A001221, A119663.
%K A380101 nonn
%O A380101 1,1
%A A380101 _Juri-Stepan Gerasimov_, Jan 12 2025