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A325992 Heinz numbers of integer partitions such that not every ordered pair of distinct parts has a different difference.

%I A325992 #9 Jun 02 2019 23:41:06
%S A325992 30,60,90,105,110,120,150,180,210,220,238,240,270,273,300,315,330,360,
%T A325992 385,390,420,440,450,462,476,480,506,510,525,540,546,550,570,600,627,
%U A325992 630,660,690,714,720,735,750,770,780,806,810,819,840,858,870,880,900,910
%N A325992 Heinz numbers of integer partitions such that not every ordered pair of distinct parts has a different difference.
%C A325992 The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%e A325992 The sequence of terms together with their prime indices begins:
%e A325992    30: {1,2,3}
%e A325992    60: {1,1,2,3}
%e A325992    90: {1,2,2,3}
%e A325992   105: {2,3,4}
%e A325992   110: {1,3,5}
%e A325992   120: {1,1,1,2,3}
%e A325992   150: {1,2,3,3}
%e A325992   180: {1,1,2,2,3}
%e A325992   210: {1,2,3,4}
%e A325992   220: {1,1,3,5}
%e A325992   238: {1,4,7}
%e A325992   240: {1,1,1,1,2,3}
%e A325992   270: {1,2,2,2,3}
%e A325992   273: {2,4,6}
%e A325992   300: {1,1,2,3,3}
%e A325992   315: {2,2,3,4}
%e A325992   330: {1,2,3,5}
%e A325992   360: {1,1,1,2,2,3}
%e A325992   385: {3,4,5}
%e A325992   390: {1,2,3,6}
%t A325992 Select[Range[1000],!UnsameQ@@Subtract@@@Subsets[PrimePi/@First/@FactorInteger[#],{2}]&]
%Y A325992 The subset case is A143823.
%Y A325992 The maximal case is A325879.
%Y A325992 The integer partition case is A325858.
%Y A325992 The strict integer partition case is A325876.
%Y A325992 Heinz numbers of the counterexamples are given by A325992.
%Y A325992 Cf. A002033, A056239, A108917, A112798, A143824, A325325, A325868, A325879, A325991, A325993, A325994.
%K A325992 nonn
%O A325992 1,1
%A A325992 _Gus Wiseman_, Jun 02 2019