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a(n) is the smallest number with exactly n divisors that are centered n-gonal numbers.
3

%I #17 Dec 24 2022 22:28:46

%S 20,325,912,43771,234784,11025,680680,9143308361,2470852896

%N a(n) is the smallest number with exactly n divisors that are centered n-gonal numbers.

%C Any subsequent terms are > 10^10. - _Lucas A. Brown_, Dec 24 2022

%H Lucas A. Brown, <a href="https://github.com/lucasaugustus/oeis/blob/main/figuratedivisors.py">Python program</a>.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CenteredPolygonalNumber.html">Centered Polygonal Number</a>

%H <a href="/index/Di#divisors">Index entries for sequences related to divisors of numbers</a>

%e a(5) = 912 because 912 has 5 centered pentagonal divisors {1, 6, 16, 76, 456} and this is the smallest such number.

%Y Cf. A005179, A358539, A358540, A358544, A358545.

%K nonn,more

%O 3,1

%A _Ilya Gutkovskiy_, Nov 21 2022

%E a(10)-a(11) from _Martin Ehrenstein_, Dec 04 2022