A327473 - OEIS

%I #5 Sep 13 2019 17:04:29

%S 2,3,4,5,7,8,9,11,13,16,17,19,23,25,27,29,30,31,32,37,41,43,47,49,53,

%T 59,61,64,67,71,73,79,81,83,84,89,90,97,101,103,105,107,109,110,113,

%U 121,125,127,128,131,137,139,149,151,157,163,167,169,173,179,181

%N Heinz numbers of integer partitions whose mean A326567/A326568 is a part.

%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    2: {1}

%e    3: {2}

%e    4: {1,1}

%e    5: {3}

%e    7: {4}

%e    8: {1,1,1}

%e    9: {2,2}

%e   11: {5}

%e   13: {6}

%e   16: {1,1,1,1}

%e   17: {7}

%e   19: {8}

%e   23: {9}

%e   25: {3,3}

%e   27: {2,2,2}

%e   29: {10}

%e   30: {1,2,3}

%e   31: {11}

%e   32: {1,1,1,1,1}

%e   37: {12}

%t primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];

%t Select[Range[100],MemberQ[primeMS[#],Mean[primeMS[#]]]&]

%Y A subsequence of A316413.

%Y Complement of A327476.

%Y The enumeration of these partitions by sum is given by A237984.

%Y Subsets whose mean is a part are A065795.

%Y Numbers whose binary indices include their mean are A327478.

%Y Cf. A000016, A056239, A067538, A112798, A240850, A325706, A326567/A326568.

%K nonn

%O 1,1

%A _Gus Wiseman_, Sep 13 2019