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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
1, 6, 6, 6, 6, 6, 6, 6, 103327500, 1977230170, 214596675756, 2796022463625, 32291440570378, 32291440570378, 549091407981061, 4680505857819681, 96914999755056255, 96914999755056255
OFFSET
1,2
EXAMPLE
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
KEYWORD
nonn,hard,more
AUTHOR
Shyam Sunder Gupta, Aug 23 2024
STATUS
approved