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A325259 Numbers with one fewer distinct prime exponents than distinct prime factors. 5
6, 10, 14, 15, 21, 22, 26, 33, 34, 35, 36, 38, 39, 46, 51, 55, 57, 58, 60, 62, 65, 69, 74, 77, 82, 84, 85, 86, 87, 90, 91, 93, 94, 95, 100, 106, 111, 115, 118, 119, 120, 122, 123, 126, 129, 132, 133, 134, 140, 141, 142, 143, 145, 146, 150, 155, 156, 158, 159 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..59.

FORMULA

A001221(a(n)) = A071625(a(n)) + 1.

EXAMPLE

The sequence of terms together with their prime indices begins:

    6: {1,2}

   10: {1,3}

   14: {1,4}

   15: {2,3}

   21: {2,4}

   22: {1,5}

   26: {1,6}

   33: {2,5}

   34: {1,7}

   35: {3,4}

   36: {1,1,2,2}

   38: {1,8}

   39: {2,6}

   46: {1,9}

   51: {2,7}

   55: {3,5}

   57: {2,8}

   58: {1,10}

   60: {1,1,2,3}

   62: {1,11}

MATHEMATICA

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

CROSSREFS

Cf. A056239, A060687, A090858, A112798, A116608, A118914, A130091, A323023, A325241, A325242, A325244, A325270, A325281.

Sequence in context: A120944 A052053 A276818 * A320911 A238748 A268390

Adjacent sequences:  A325254 A325256 A325258 * A325260 A325261 A325262

KEYWORD

nonn

AUTHOR

Gus Wiseman, Apr 18 2019

STATUS

approved

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Last modified July 22 10:34 EDT 2019. Contains 325219 sequences. (Running on oeis4.)