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A374503
Positive triangular numbers such that the two numbers before it and the two numbers after it are squarefree.
1
36, 300, 780, 1596, 2016, 2556, 2628, 3240, 3828, 4560, 5460, 6216, 7260, 8256, 9180, 10296, 10440, 11628, 12720, 14196, 16836, 18336, 18528, 21528, 23220, 23436, 25200, 26796, 28680, 32640, 34716, 34980, 37128, 39060, 41616, 43956, 46056, 48516, 48828, 51360, 53628, 56280, 64980, 67896, 70500
OFFSET
1,1
COMMENTS
All terms of this sequence are divisible by 4, so they can't be squarefree.
LINKS
EXAMPLE
36 = 2^2 * 3^2 (the 8th triangular number) between 34 = 2 * 17, 35 = 5 * 7 and 37 which is a prime number, 38 = 2 * 19.
300 = 2^2 * 3 * 5^2 (the 24th triangular number) between 298 = 2 * 149, 299 = 13 * 23 and 301 = 7 * 43, 302 = 2 * 151.
780 = 2^2 * 3 * 5 * 13 (the 39th triangular number) between 778 = 2 * 389, 779 = 19 * 41 and 781 = 11 * 71, 782 = 2 * 17 * 23.
MAPLE
select(t -> andmap(numtheory:-issqrfree, [t-2, t-1, t+1, t+2]), [seq(seq((8*t+i)*(8*t+i+1)/2, i=[-1, 0]), t=1..100)]); # Robert Israel, Jan 31 2025
MATHEMATICA
Select[Accumulate[Range[400]], And @@ (SquareFreeQ /@ (# + {-2, -1, 1, 2})) &] (* Amiram Eldar, Jul 09 2024 *)
CROSSREFS
Sequence in context: A226836 A218647 A067741 * A185096 A073972 A219633
KEYWORD
nonn,changed
AUTHOR
Massimo Kofler, Jul 09 2024
STATUS
approved