|
%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
|
