cp's OEIS Frontend

A325270 Numbers with 1 fewer distinct prime exponents than (not necessarily distinct) prime factors.

%I A325270 #11 Jul 05 2019 04:05:01
%S A325270 4,6,9,10,12,14,15,18,20,21,22,25,26,28,33,34,35,38,39,44,45,46,49,50,
%T A325270 51,52,55,57,58,62,63,65,68,69,74,75,76,77,82,85,86,87,91,92,93,94,95,
%U A325270 98,99,106,111,115,116,117,118,119,121,122,123,124,129,133
%N A325270 Numbers with 1 fewer distinct prime exponents than (not necessarily distinct) prime factors.
%C A325270 Also Heinz numbers of integer partitions with 1 fewer distinct multiplicities than parts, where the Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k). The enumeration of these partitions by sum is given by A117571.
%C A325270 Also numbers whose sorted prime signature is (1,1), (2), or (1,2). - _Gus Wiseman_, Jul 03 2019
%e A325270 The sequence of terms together with their prime indices begins:
%e A325270     4: {1,1}
%e A325270     6: {1,2}
%e A325270     9: {2,2}
%e A325270    10: {1,3}
%e A325270    12: {1,1,2}
%e A325270    14: {1,4}
%e A325270    15: {2,3}
%e A325270    18: {1,2,2}
%e A325270    20: {1,1,3}
%e A325270    21: {2,4}
%e A325270    22: {1,5}
%e A325270    25: {3,3}
%e A325270    26: {1,6}
%e A325270    28: {1,1,4}
%e A325270    33: {2,5}
%e A325270    34: {1,7}
%e A325270    35: {3,4}
%e A325270    38: {1,8}
%e A325270    39: {2,6}
%e A325270    44: {1,1,5}
%t A325270 Select[Range[100],PrimeOmega[#]==Length[Union[Last/@FactorInteger[#]]]+1&]
%Y A325270 Cf. A001221, A001222, A000961, A005117, A060687, A062770, A071625, A072774, A090858, A117571, A118914, A130091, A325244, A325259.
%K A325270 nonn
%O A325270 1,1
%A A325270 _Gus Wiseman_, Apr 18 2019