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%I #6 Apr 10 2019 22:02:51
%S 5,8,10,12,20,21,35,36,42,49,54,60,63,70,81,84,90,98,100,105,126,135,
%T 140,147,150,189,196,210,225,275,294,315,385,441,500,539,550,605,700,
%U 750,770,825,847,980,1050,1078,1100,1125,1155,1210,1250,1331,1372,1375
%N Heinz number of integer partitions such that the difference between the length of the minimal square containing and the maximal square contained in the Young diagram is 2.
%C The enumeration of these partitions by sum is given by A325182.
%C The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%H Gus Wiseman, <a href="/A325180/a325180.png">Young diagrams corresponding to the first 96 terms</a>.
%e The sequence of terms together with their prime indices begins:
%e 5: {3}
%e 8: {1,1,1}
%e 10: {1,3}
%e 12: {1,1,2}
%e 20: {1,1,3}
%e 21: {2,4}
%e 35: {3,4}
%e 36: {1,1,2,2}
%e 42: {1,2,4}
%e 49: {4,4}
%e 54: {1,2,2,2}
%e 60: {1,1,2,3}
%e 63: {2,2,4}
%e 70: {1,3,4}
%e 81: {2,2,2,2}
%e 84: {1,1,2,4}
%e 90: {1,2,2,3}
%e 98: {1,4,4}
%e 100: {1,1,3,3}
%e 105: {2,3,4}
%t durf[n_]:=Length[Select[Range[PrimeOmega[n]],Reverse[Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]][[#]]>=#&]];
%t codurf[n_]:=If[n==1,0,Max[PrimeOmega[n],PrimePi[FactorInteger[n][[-1,1]]]]];
%t Select[Range[1000],codurf[#]-durf[#]==2&]
%Y Numbers k such that A263297(k) - A257990(k) = 2.
%Y Positions of 2's in A325178.
%Y Cf. A006918, A056239, A093641, A112798, A325164, A325170, A325179, A325182, A325192, A325197.
%K nonn
%O 1,1
%A _Gus Wiseman_, Apr 08 2019
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