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A327775 Heinz numbers of integer partitions whose LCM is twice their sum. 5
154, 190, 435, 580, 714, 952, 1118, 1287, 1430, 1653, 1716, 1815, 1935, 2067, 2150, 2204, 2254, 2288, 2415, 2475, 2580, 2756, 2898, 2970, 3220, 3300, 3440, 3710, 3864, 3960, 3975, 4770, 5152, 5280, 5300, 6360, 6461, 6897, 7514, 8307, 8480, 8619, 8695, 8778 (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).

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..1000

FORMULA

A290103(a(k)) = 2 * A056239(a(k)).

EXAMPLE

The sequence of terms together with their prime indices begins:

   154: {1,4,5}

   190: {1,3,8}

   435: {2,3,10}

   580: {1,1,3,10}

   714: {1,2,4,7}

   952: {1,1,1,4,7}

  1118: {1,6,14}

  1287: {2,2,5,6}

  1430: {1,3,5,6}

  1653: {2,8,10}

  1716: {1,1,2,5,6}

  1815: {2,3,5,5}

  1935: {2,2,3,14}

  2067: {2,6,16}

  2150: {1,3,3,14}

  2204: {1,1,8,10}

  2254: {1,4,4,9}

  2288: {1,1,1,1,5,6}

  2415: {2,3,4,9}

  2475: {2,2,3,3,5}

MAPLE

q:= n-> (l-> is(ilcm(l[])=2*add(j, j=l)))(map(i->

        numtheory[pi](i[1])$i[2], ifactors(n)[2])):

select(q, [$1..10000])[];  # Alois P. Heinz, Sep 27 2019

MATHEMATICA

primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];

Select[Range[2, 1000], LCM@@primeMS[#]==2*Total[primeMS[#]]&]

CROSSREFS

The enumeration of these partitions by sum is A327780.

Heinz numbers of partitions whose LCM is less than their sum are A327776.

Heinz numbers of partitions whose LCM is a multiple their sum are A327783.

Heinz numbers of partitions whose LCM is greater than their sum are A327784.

Cf. A056239, A074761, A112798, A290103, A326841 , A327778.

Sequence in context: A049515 A049519 A214475 * A053243 A320708 A261377

Adjacent sequences:  A327772 A327773 A327774 * A327776 A327777 A327778

KEYWORD

nonn

AUTHOR

Gus Wiseman, Sep 25 2019

STATUS

approved

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Last modified June 24 02:56 EDT 2021. Contains 345415 sequences. (Running on oeis4.)