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 A325991 Heinz numbers of integer partitions such that not every orderless pair of distinct parts has a different sum. 7

%I

%S 210,420,462,630,840,858,910,924,1050,1155,1260,1326,1386,1470,1680,

%T 1716,1820,1848,1870,1890,1938,2100,2145,2310,2470,2520,2574,2622,

%U 2652,2730,2772,2926,2940,3150,3234,3315,3360,3432,3465,3570,3640,3696,3740,3780,3876

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

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

%e 420: {1,1,2,3,4}

%e 462: {1,2,4,5}

%e 630: {1,2,2,3,4}

%e 840: {1,1,1,2,3,4}

%e 858: {1,2,5,6}

%e 910: {1,3,4,6}

%e 924: {1,1,2,4,5}

%e 1050: {1,2,3,3,4}

%e 1155: {2,3,4,5}

%e 1260: {1,1,2,2,3,4}

%e 1326: {1,2,6,7}

%e 1386: {1,2,2,4,5}

%e 1470: {1,2,3,4,4}

%e 1680: {1,1,1,1,2,3,4}

%e 1716: {1,1,2,5,6}

%e 1820: {1,1,3,4,6}

%e 1848: {1,1,1,2,4,5}

%e 1870: {1,3,5,7}

%e 1890: {1,2,2,2,3,4}

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

%Y The subset case is A196723.

%Y The maximal case is A325878.

%Y The integer partition case is A325857.

%Y The strict integer partition case is A325877.

%Y Heinz numbers of the counterexamples are given by A325991.

%Y Cf. A002033, A056239, A103300, A108917, A112798, A143823, A196724, A325853, A325855, A325858, A325859, A325862, A325992, A325993, A325994.

%K nonn

%O 1,1

%A _Gus Wiseman_, Jun 02 2019

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Last modified March 29 21:32 EDT 2020. Contains 333117 sequences. (Running on oeis4.)