A358540
a(n) is the smallest number with exactly n divisors that are n-gonal pyramidal numbers.
Original entry on oeis.org
56, 140, 1440, 11550, 351120, 41580, 742560, 29279250, 8316000, 72348396120, 3386892600, 578918340
Offset: 3
a(5) = 1440 because 1440 has 5 pentagonal pyramidal divisors {1, 6, 18, 40, 288} and this is the smallest such number.
A358541
a(n) is the smallest number with exactly n divisors that are centered n-gonal numbers.
Original entry on oeis.org
20, 325, 912, 43771, 234784, 11025, 680680, 9143308361, 2470852896
Offset: 3
a(5) = 912 because 912 has 5 centered pentagonal divisors {1, 6, 16, 76, 456} and this is the smallest such number.
A358859
a(n) is the smallest n-gonal number divisible by exactly n n-gonal numbers.
Original entry on oeis.org
6, 36, 210, 4560, 6426, 326040, 4232250, 1969110, 296676380, 4798080, 166289760, 73765692000, 712750500, 50561280, 33944067893736, 2139168754800, 4292572951800, 1414764341760, 72461756727360, 180975331456920, 1870768457500800, 5498331930000, 153698278734000
Offset: 3
a(5) = 210, because 210 is a pentagonal number that has 5 pentagonal divisors {1, 5, 35, 70, 210} and this is the smallest such number.
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a(n) = if(n<3, return()); for(k=1, oo, my(t=(k*(n*k - n - 2*k + 4))\2); if(sumdiv(t, d, ispolygonal(d, n)) == n, return(t))); \\ Daniel Suteu, Dec 04 2022
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