A375658 The smallest triangular number that begins a run of at least n consecutive triangular numbers with the same number of distinct prime factors.

1, 6, 6, 6, 6, 6, 6, 6, 103327500, 1977230170, 214596675756, 2796022463625, 32291440570378, 32291440570378, 549091407981061, 4680505857819681, 96914999755056255, 96914999755056255

Offset: 1

Author

Shyam Sunder Gupta, Aug 23 2024

Keywords

• nonn
• hard
• more

Examples

			a(8) = 6 because 6 is the smallest triangular number that begins a run of 8 consecutive triangular numbers (6, 10, 15, 21, 28, 36, 45, 55) with the same number of distinct prime factors, i.e. 2.
a(9) = 103327500 because 103327500 is the smallest triangular number that begins a run of 9 consecutive triangular numbers (103327500, 103341876, 103356253, 103370631, 103385010, 103399390,  103413771, 103428153, 103442536) with the same number of distinct prime factors, i.e. 5.
		

Crossrefs

Cf. A000217, A069903, A076551.

Cf. A375657.