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A325179 Heinz numbers 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 1.

%I A325179 #6 Apr 10 2019 22:03:00
%S A325179 3,4,6,15,18,25,27,30,45,50,75,175,245,250,343,350,375,490,525,625,
%T A325179 686,735,875,1029,1225,1715,3773,4802,5929,7203,7546,9317,11319,11858,
%U A325179 12005,14641,16807,17787,18634,18865,26411,27951,29282,29645,41503,43923,46585
%N A325179 Heinz numbers 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 1.
%C A325179 The enumeration of these partitions by sum is given by A325181.
%C A325179 The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%H A325179 Gus Wiseman, <a href="/A325179/a325179.png">Young diagrams for the first 32 terms</a>.
%e A325179 The sequence of terms together with their prime indices begins:
%e A325179     3: {2}
%e A325179     4: {1,1}
%e A325179     6: {1,2}
%e A325179    15: {2,3}
%e A325179    18: {1,2,2}
%e A325179    25: {3,3}
%e A325179    27: {2,2,2}
%e A325179    30: {1,2,3}
%e A325179    45: {2,2,3}
%e A325179    50: {1,3,3}
%e A325179    75: {2,3,3}
%e A325179   175: {3,3,4}
%e A325179   245: {3,4,4}
%e A325179   250: {1,3,3,3}
%e A325179   343: {4,4,4}
%e A325179   350: {1,3,3,4}
%e A325179   375: {2,3,3,3}
%e A325179   490: {1,3,4,4}
%e A325179   525: {2,3,3,4}
%e A325179   625: {3,3,3,3}
%t A325179 durf[n_]:=Length[Select[Range[PrimeOmega[n]],Reverse[Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]][[#]]>=#&]];
%t A325179 codurf[n_]:=If[n==1,0,Max[PrimeOmega[n],PrimePi[FactorInteger[n][[-1,1]]]]];
%t A325179 Select[Range[1000],codurf[#]-durf[#]==1&]
%Y A325179 Numbers k such that A263297(k) - A257990(k) = 1.
%Y A325179 Positions of 1's in A325178.
%Y A325179 Cf. A056239, A093641, A112798, A325180, A325181, A325192, A325196, A325198.
%K A325179 nonn
%O A325179 1,1
%A A325179 _Gus Wiseman_, Apr 08 2019