cp's OEIS Frontend

A325259 Numbers with one fewer distinct prime exponents than distinct prime factors.

%I A325259 #4 Apr 18 2019 16:54:35
%S A325259 6,10,14,15,21,22,26,33,34,35,36,38,39,46,51,55,57,58,60,62,65,69,74,
%T A325259 77,82,84,85,86,87,90,91,93,94,95,100,106,111,115,118,119,120,122,123,
%U A325259 126,129,132,133,134,140,141,142,143,145,146,150,155,156,158,159
%N A325259 Numbers with one fewer distinct prime exponents than distinct prime factors.
%C A325259 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 A325259 A001221(a(n)) = A071625(a(n)) + 1.
%e A325259 The sequence of terms together with their prime indices begins:
%e A325259     6: {1,2}
%e A325259    10: {1,3}
%e A325259    14: {1,4}
%e A325259    15: {2,3}
%e A325259    21: {2,4}
%e A325259    22: {1,5}
%e A325259    26: {1,6}
%e A325259    33: {2,5}
%e A325259    34: {1,7}
%e A325259    35: {3,4}
%e A325259    36: {1,1,2,2}
%e A325259    38: {1,8}
%e A325259    39: {2,6}
%e A325259    46: {1,9}
%e A325259    51: {2,7}
%e A325259    55: {3,5}
%e A325259    57: {2,8}
%e A325259    58: {1,10}
%e A325259    60: {1,1,2,3}
%e A325259    62: {1,11}
%t A325259 Select[Range[100],PrimeNu[#]==Length[Union[Last/@FactorInteger[#]]]+1&]
%Y A325259 Cf. A056239, A060687, A090858, A112798, A116608, A118914, A130091, A323023, A325241, A325242, A325244, A325270, A325281.
%K A325259 nonn
%O A325259 1,1
%A A325259 _Gus Wiseman_, Apr 18 2019