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A325270 Numbers with 1 fewer distinct prime exponents than (not necessarily distinct) prime factors. 6

%I #11 Jul 05 2019 04:05:01

%S 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 51,52,55,57,58,62,63,65,68,69,74,75,76,77,82,85,86,87,91,92,93,94,95,

%U 98,99,106,111,115,116,117,118,119,121,122,123,124,129,133

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

%C 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 Also numbers whose sorted prime signature is (1,1), (2), or (1,2). - _Gus Wiseman_, Jul 03 2019

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

%e 4: {1,1}

%e 6: {1,2}

%e 9: {2,2}

%e 10: {1,3}

%e 12: {1,1,2}

%e 14: {1,4}

%e 15: {2,3}

%e 18: {1,2,2}

%e 20: {1,1,3}

%e 21: {2,4}

%e 22: {1,5}

%e 25: {3,3}

%e 26: {1,6}

%e 28: {1,1,4}

%e 33: {2,5}

%e 34: {1,7}

%e 35: {3,4}

%e 38: {1,8}

%e 39: {2,6}

%e 44: {1,1,5}

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

%Y Cf. A001221, A001222, A000961, A005117, A060687, A062770, A071625, A072774, A090858, A117571, A118914, A130091, A325244, A325259.

%K nonn

%O 1,1

%A _Gus Wiseman_, Apr 18 2019

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Last modified March 28 14:21 EDT 2024. Contains 371254 sequences. (Running on oeis4.)