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a(n) is the smallest number with exactly n divisors that are n-gonal pyramidal numbers.
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%I #26 Dec 25 2022 02:13:22

%S 56,140,1440,11550,351120,41580,742560,29279250,8316000,72348396120,

%T 3386892600,578918340

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

%C Any subsequent terms are > 2 * 10^9. - _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/PyramidalNumber.html">Pyramidal Number</a>

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

%e a(5) = 1440 because 1440 has 5 pentagonal pyramidal divisors {1, 6, 18, 40, 288} and this is the smallest such number.

%Y Cf. A005179, A358539, A358541, A358542, A358543.

%K nonn,more

%O 3,1

%A _Ilya Gutkovskiy_, Nov 21 2022

%E a(11)-a(13) from _Martin Ehrenstein_, Dec 02 2022

%E a(14) from _Lucas A. Brown_, Dec 19 2022