A325992 - OEIS

%I #9 Jun 02 2019 23:41:06

%S 30,60,90,105,110,120,150,180,210,220,238,240,270,273,300,315,330,360,

%T 385,390,420,440,450,462,476,480,506,510,525,540,546,550,570,600,627,

%U 630,660,690,714,720,735,750,770,780,806,810,819,840,858,870,880,900,910

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

%C The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).

%e The sequence of terms together with their prime indices begins:

%e    30: {1,2,3}

%e    60: {1,1,2,3}

%e    90: {1,2,2,3}

%e   105: {2,3,4}

%e   110: {1,3,5}

%e   120: {1,1,1,2,3}

%e   150: {1,2,3,3}

%e   180: {1,1,2,2,3}

%e   210: {1,2,3,4}

%e   220: {1,1,3,5}

%e   238: {1,4,7}

%e   240: {1,1,1,1,2,3}

%e   270: {1,2,2,2,3}

%e   273: {2,4,6}

%e   300: {1,1,2,3,3}

%e   315: {2,2,3,4}

%e   330: {1,2,3,5}

%e   360: {1,1,1,2,2,3}

%e   385: {3,4,5}

%e   390: {1,2,3,6}

%t Select[Range[1000],!UnsameQ@@Subtract@@@Subsets[PrimePi/@First/@FactorInteger[#],{2}]&]

%Y The subset case is A143823.

%Y The maximal case is A325879.

%Y The integer partition case is A325858.

%Y The strict integer partition case is A325876.

%Y Heinz numbers of the counterexamples are given by A325992.

%Y Cf. A002033, A056239, A108917, A112798, A143824, A325325, A325868, A325879, A325991, A325993, A325994.

%K nonn

%O 1,1

%A _Gus Wiseman_, Jun 02 2019