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 A325180 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. 7

%I

%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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Last modified November 27 15:11 EST 2020. Contains 338683 sequences. (Running on oeis4.)