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A374372
Pentagonal numbers that are products of smaller pentagonal numbers.
3
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
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.
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
KEYWORD
nonn
AUTHOR
STATUS
approved