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A325270 Numbers with 1 fewer distinct prime exponents than (not necessarily distinct) prime factors. 6
4, 6, 9, 10, 12, 14, 15, 18, 20, 21, 22, 25, 26, 28, 33, 34, 35, 38, 39, 44, 45, 46, 49, 50, 51, 52, 55, 57, 58, 62, 63, 65, 68, 69, 74, 75, 76, 77, 82, 85, 86, 87, 91, 92, 93, 94, 95, 98, 99, 106, 111, 115, 116, 117, 118, 119, 121, 122, 123, 124, 129, 133 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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.

Also numbers whose sorted prime signature is (1,1), (2), or (1,2). - Gus Wiseman, Jul 03 2019

LINKS

Table of n, a(n) for n=1..62.

EXAMPLE

The sequence of terms together with their prime indices begins:

    4: {1,1}

    6: {1,2}

    9: {2,2}

   10: {1,3}

   12: {1,1,2}

   14: {1,4}

   15: {2,3}

   18: {1,2,2}

   20: {1,1,3}

   21: {2,4}

   22: {1,5}

   25: {3,3}

   26: {1,6}

   28: {1,1,4}

   33: {2,5}

   34: {1,7}

   35: {3,4}

   38: {1,8}

   39: {2,6}

   44: {1,1,5}

MATHEMATICA

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

CROSSREFS

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

Sequence in context: A174896 A304634 A319240 * A051278 A175127 A174166

Adjacent sequences:  A325267 A325268 A325269 * A325271 A325272 A325273

KEYWORD

nonn

AUTHOR

Gus Wiseman, Apr 18 2019

STATUS

approved

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Last modified August 21 04:54 EDT 2019. Contains 326162 sequences. (Running on oeis4.)