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%I #11 Feb 27 2018 20:03:13
%S 1,1,1,2,1,4,1,4,6,6,1,12,1,8,16,8,1,28,1,24,30,10,1,32,22,12,44,40,1,
%T 96,1,16,48,14,68,96,1,16,70,80,1,220,1,60,204,18,1,80,90,168,96,84,1,
%U 224,146,160,126,20,1,400,1,22,584,32,264,416,1,112,160
%N Number of normal semistandard Young tableaux whose shape is the conjugate of the integer partition with Heinz number n.
%C A tableau is normal if its entries span an initial interval of positive integers. The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%t a[n_]:=If[n===1,1,Sum[a[n/q*Times@@Cases[FactorInteger[q],{p_,k_}:>If[p===2,1,NextPrime[p,-1]^k]]],{q,Rest[Divisors[n]]}]];
%t Array[a,100]
%Y Cf. A000085, A001222, A056239, A063834, A112798, A122111, A138178, A153452, A191714, A210391, A228125, A296150, A296188, A299202.
%K nonn
%O 1,4
%A _Gus Wiseman_, Feb 15 2018
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