A303339 a(n) is the largest triangular number that is prime(n)-smooth.

1, 36, 3240, 9568125, 48024900, 7589181600, 56495217870, 70320436841655, 70320436841655, 15696858221890560, 1298157862542190650, 5996877118268400000, 2043364250317598208000, 88678944280899462664980, 615491489313111203244375, 1056447213455901684717300

Offset

1,2

Links

Table of n, a(n) for n=1..16.

Formula

a(n) = A000217(A002072(n)).

Example

The first prime is 2, and the only triangular number that is 2-smooth is 1, so a(1) = 1.
The second prime is 3, and the only triangular numbers that are 3-smooth are 1, 3, 6 = 2 * 3, and 36 = 2^2 * 3^2, so a(2) = 2.
The third prime is 5, and the only triangular numbers that are 5-smooth are the 3-smooth triangular numbers and 10 = 2 * 5, 15 = 3 * 5, 45 = 3^2 * 5, 120 = 2^3 * 3 * 5, 300 = 2^2 * 3 * 5^2, and 3240 = 2^3 * 3^4 * 5, so a(3) = 3240.

Crossrefs

Cf. A000217, A002072.

Sequence in context: A036510 A232669 A338076 * A034983 A291911 A072377

Adjacent sequences: A303336 A303337 A303338 * A303340 A303341 A303342

Keyword

nonn

Author

Jon E. Schoenfield, Apr 22 2018

Status

approved