A374372 - OEIS

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A374372

Pentagonal numbers that are products of smaller pentagonal numbers.

1, 10045, 11310, 20475, 52360, 197472, 230300, 341055, 367290, 836640, 2437800, 2939300, 3262700, 4048352, 4268110, 4293450, 4619160, 4816000, 5969040, 6192520, 6913340, 6997320, 8531145, 10933650, 12397000, 16008300, 18573282, 18816875, 21430710, 24383520

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OFFSET

1,2

COMMENTS

There are infinitely many terms where the corresponding product has two factors. This can be seen by solving the equation A000326(x)=A000326(y)*A000326(z) for a fixed z for which a solution exists, leading to a generalized Pell equation. For example, z = 5 leads to the solutions (x,y) = (82,14), (1649982,278898), (33266933642,5623138102), ..., corresponding to the terms A000326(82) = 10045, A000326(1649982) = 4083660075495, A000326(33266933642) = 1660033310895213609425, ... in the sequence.

LINKS

Table of n, a(n) for n=1..30.

EXAMPLE

1 is a term because it is a pentagonal number and equals the empty product.

10045 is a term because it is a pentagonal number and equals the product of the pentagonal numbers 35 and 287.

20475 is a term because it is a pentagonal number and equals the product of the pentagonal numbers 5, 35, and 117. (This is the first term that requires more than two factors.)

CROSSREFS

Row n=5 of A374370.

A188663 is a subsequence (only 2 factors allowed).

Cf. A000326.

Sequence in context: A213318 A346026 A097648 * A188663 A250711 A223431

Adjacent sequences: A374369 A374370 A374371 * A374373 A374374 A374375

KEYWORD

nonn

AUTHOR

Pontus von Brömssen, Jul 07 2024

STATUS

approved