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A350405 a(n) is the smallest number which can be represented as the sum of n distinct nonzero n-gonal numbers in exactly n ways, or 0 if no such number exists.

%I A350405 #21 Feb 16 2025 08:34:02
%S A350405 37,142,285,536,911,1268,1909,2713,3876,5179,6891,8901,11190,14384,
%T A350405 18087,21697,27055,32166,39111,46560,53892,64412,73949,86778,98202,
%U A350405 113635,130088,148051,167505,190968,214955,240143,269775,297615,331201,367429,409179,451340,497830
%N A350405 a(n) is the smallest number which can be represented as the sum of n distinct nonzero n-gonal numbers in exactly n ways, or 0 if no such number exists.
%H A350405 David A. Corneth, <a href="/A350405/b350405.txt">Table of n, a(n) for n = 3..102</a>
%H A350405 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PolygonalNumber.html">Polygonal Number</a>
%F A350405 a(n) >= A006484(n). - _David A. Corneth_, Dec 30 2021
%e A350405 For n = 3: 37 = 1 + 15 + 21 = 3 + 6 + 28 = 6 + 10 + 21.
%t A350405 Do[i=1;While[b=PolygonalNumber[n,Range@i++];!IntegerQ[t=Min[First/@Select[Tally[Select[Total/@Subsets[b,{n}],#<=Max@b&]],Last@#==n&]]]];Print@t,{n,3,10}] (* _Giorgos Kalogeropoulos_, Dec 30 2021 *)
%Y A350405 Cf. A006484, A025443, A057145, A307598, A350207, A350241, A350288.
%K A350405 nonn
%O A350405 3,1
%A A350405 _Ilya Gutkovskiy_, Dec 29 2021
%E A350405 a(10)-a(31) from _Michael S. Branicky_, Dec 29 2021
%E A350405 More terms from _David A. Corneth_, Dec 30 2021