A325259 - OEIS

%I #4 Apr 18 2019 16:54:35

%S 6,10,14,15,21,22,26,33,34,35,36,38,39,46,51,55,57,58,60,62,65,69,74,

%T 77,82,84,85,86,87,90,91,93,94,95,100,106,111,115,118,119,120,122,123,

%U 126,129,132,133,134,140,141,142,143,145,146,150,155,156,158,159

%N Numbers with one fewer distinct prime exponents than distinct prime factors.

%C The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k), so these are Heinz numbers of integer partitions with one fewer distinct multiplicities than distinct parts. The enumeration of these partitions by sum is given by A325244.

%F A001221(a(n)) = A071625(a(n)) + 1.

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

%e     6: {1,2}

%e    10: {1,3}

%e    14: {1,4}

%e    15: {2,3}

%e    21: {2,4}

%e    22: {1,5}

%e    26: {1,6}

%e    33: {2,5}

%e    34: {1,7}

%e    35: {3,4}

%e    36: {1,1,2,2}

%e    38: {1,8}

%e    39: {2,6}

%e    46: {1,9}

%e    51: {2,7}

%e    55: {3,5}

%e    57: {2,8}

%e    58: {1,10}

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

%e    62: {1,11}

%t Select[Range[100],PrimeNu[#]==Length[Union[Last/@FactorInteger[#]]]+1&]

%Y Cf. A056239, A060687, A090858, A112798, A116608, A118914, A130091, A323023, A325241, A325242, A325244, A325270, A325281.

%K nonn

%O 1,1

%A _Gus Wiseman_, Apr 18 2019