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a(n) is the least integer that is pyramidal in exactly n ways.
2

%I #20 Apr 12 2020 10:25:18

%S 4,10,30,550,1540,48070,223300,2634940,402610950,1570545340,

%T 13960282700,5677137442900,248297918605660

%N a(n) is the least integer that is pyramidal in exactly n ways.

%C a(n) has exactly n representations as an m-gonal pyramidal number P(m, k) = k*(k + 1)*(k*(m - 2) - m + 5) / 6, with m > 2, k > 1.

%C a(12) > 5*10^11. - _Giovanni Resta_, Apr 11 2020

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PyramidalNumber.html">Pyramidal Number</a>

%H <a href="/index/Ps#pyramidal_numbers">Index to sequences related to pyramidal numbers</a>

%e a(3) = 30 because 30 is the least integer which is pyramidal in 3 ways (30 is the fourth square pyramidal number, the third octagonal pyramidal number and also the second 31-gonal pyramidal number).

%Y Cf. A063778, A080851, A261720, A333915.

%K nonn,more

%O 1,1

%A _Ilya Gutkovskiy_, Apr 09 2020

%E a(9) from _Jinyuan Wang_, Apr 10 2020

%E a(10)-a(11) from _Giovanni Resta_, Apr 10 2020

%E a(12)-a(13) from _Bert Dobbelaere_, Apr 12 2020