%I #11 Dec 31 2022 15:18:15
%S 0,2,4,5,7,12,16,17,22,24,32,42,53,65,79,96,114,134,155,180,205,233,
%T 263,294,329,364,403,442,485,529,576,625,676,729,785,842,902,964,1029,
%U 1097,1167,1238,1313,1390,1469,1552,1636,1723,1813,1904,1999,2096,2195,2298
%N Irregular triangle read by rows: the n-th row gives the exponents of the powers of x corresponding to the maximal coefficient of the product x^2*(x^2 + x^3)*(x^2 + x^3 + x^5)*...*(x^2 + x^3 + x^5 + ... + x^prime(n)).
%C Conjecture: except for n = 2, 5, and 6, the rows have length equal to 1.
%e The irregular triangle begins:
%e 0;
%e 2;
%e 4, 5;
%e 7;
%e 12;
%e 16, 17;
%e 22, 24;
%e 32;
%e 42;
%e 53;
%e 65;
%e ...
%t b[n_]:=CoefficientList[Product[Sum[x^Prime[i],{i,k}],{k,n}],x]; Table[Position[b[n],Max[b[n]]]-1,{n,0,50}]//Flatten
%Y Cf. A000040, A359328.
%Y Cf. A359338 (minimal exponent), A359339 (maximal exponent).
%K nonn,tabf
%O 0,2
%A _Stefano Spezia_, Dec 27 2022