A325761 - OEIS

%I #5 May 18 2019 22:46:51

%S 1,2,6,9,15,20,21,30,33,39,45,50,51,56,57,69,70,75,84,87,93,105,110,

%T 111,123,125,126,129,130,140,141,159,165,170,175,176,177,183,189,190,

%U 195,196,201,210,213,219,230,237,245,249,255,264,267,275,285,290,291

%N Heinz numbers of integer partitions whose length is itself a part.

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

%C The enumeration of these partitions by sum is given by A002865.

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

%e     1: {}

%e     2: {1}

%e     6: {1,2}

%e     9: {2,2}

%e    15: {2,3}

%e    20: {1,1,3}

%e    21: {2,4}

%e    30: {1,2,3}

%e    33: {2,5}

%e    39: {2,6}

%e    45: {2,2,3}

%e    50: {1,3,3}

%e    51: {2,7}

%e    56: {1,1,1,4}

%e    57: {2,8}

%e    69: {2,9}

%e    70: {1,3,4}

%e    75: {2,3,3}

%e    84: {1,1,2,4}

%e    87: {2,10}

%t Select[Range[100],MemberQ[PrimePi/@First/@FactorInteger[#],PrimeOmega[#]]&]

%Y Cf. A001222, A002865, A056239, A093641, A109298, A110295, A112798, A118914, A325762, A325763.

%K nonn

%O 1,2

%A _Gus Wiseman_, May 18 2019