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Least n-gonal number that can be written as a product of two or more smaller n-gonal numbers, or 0 if no such number exists.
2

%I #5 Jul 07 2024 13:51:09

%S 4,36,16,10045,2850,6426,1408,265926,69300,79135,9504,195615,145236,

%T 126630,42120,81356859,9410205,165550,1379840,11340,3009069,

%U 8321351148,316200,47555937,218338146,9042726,822528,12300400,300186051,46955700,766737400,206898615

%N Least n-gonal number that can be written as a product of two or more smaller n-gonal numbers, or 0 if no such number exists.

%e For 2 <= n <= 33, the n-gonal number a(n) can be written as a product of smaller n-gonal numbers in the following ways:

%e n | a(n)

%e ---+---------------------------

%e 2 | 4 = 2*2

%e 3 | 36 = 6*6

%e 4 | 16 = 4*4

%e 5 | 10045 = 35*287

%e 6 | 2850 = 15*190

%e 7 | 6426 = 34*189

%e 8 | 1408 = 8*176

%e 9 | 265926 = 46*5781

%e 10 | 69300 = 10*6930

%e 11 | 79135 = 95*833

%e 12 | 9504 = 33*288

%e 13 | 195615 = 115*1701

%e 14 | 145236 = 14*10374

%e 15 | 126630 = 15*42*201

%e 16 | 42120 = 45*936

%e 17 | 81356859 = 549*148191

%e 18 | 9410205 = 343*27435

%e 19 | 165550 = 175*946

%e 20 | 1379840 = 20*68992

%e 21 | 11340 = 21*540

%e 22 | 3009069 = 427*7047

%e 23 | 8321351148 = 23*66*5481786

%e 24 | 316200 = 136*2325

%e 25 | 47555937 = 351*135487

%e 26 | 218338146 = 26*8397621

%e 27 | 9042726 = 154*58719

%e 28 | 822528 = 28*29376

%e 29 | 12300400 = 764*16100

%e 30 | 300186051 = 13051*23001

%e 31 | 46955700 = 3060*15345

%e 32 | 766737400 = 5720*134045

%e 33 | 206898615 = 12615*16401

%Y Second column of A374370.

%Y Cf. A057145.

%K nonn

%O 2,1

%A _Pontus von Brömssen_, Jul 07 2024