A375657 The smallest triangular number that begins a run of at least n consecutive triangular numbers with the same number of prime factors (counted with multiplicity).

1, 6, 6, 6, 724206, 32365035, 32365035, 9127288495, 497232340606, 54524401634046, 192541553136345, 3119282531272578, 1584264619108935753, 34399764958387086910, 34399764958387086910

Offset: 1

Author

Shyam Sunder Gupta, Aug 23 2024

Keywords

• nonn
• hard
• more

Examples

			a(4) = 6 because 6 is the smallest triangular number that begins a run of 4 consecutive triangular numbers (6, 10, 15, 21) with the same number of prime factors (counted with multiplicity), i.e. 2.
a(5) = 724206 because 724206 is the smallest triangular number that begins a run of 5 consecutive triangular numbers (724206, 725410, 726615, 727821, 729028) with the same number of prime factors (counted with multiplicity), i.e. 5.
		

Crossrefs

Cf. A000217, A069904, A075088.

Cf. A375658.