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A327776 Heinz numbers of integer partitions whose LCM is less than their sum. 4
4, 6, 8, 9, 10, 12, 14, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 32, 34, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 52, 54, 56, 57, 58, 60, 62, 63, 64, 65, 68, 72, 74, 75, 76, 78, 80, 81, 82, 84, 86, 87, 88, 90, 92, 94, 96, 98, 100, 104, 106, 108, 111, 112 (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

Table of n, a(n) for n=1..64.

EXAMPLE

The sequence of terms together with their prime indices begins:

    4: {1,1}

    6: {1,2}

    8: {1,1,1}

    9: {2,2}

   10: {1,3}

   12: {1,1,2}

   14: {1,4}

   16: {1,1,1,1}

   18: {1,2,2}

   20: {1,1,3}

   21: {2,4}

   22: {1,5}

   24: {1,1,1,2}

   25: {3,3}

   26: {1,6}

   27: {2,2,2}

   28: {1,1,4}

   32: {1,1,1,1,1}

   34: {1,7}

   36: {1,1,2,2}

MAPLE

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

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

select(q, [$1..120])[];  # 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, 100], LCM@@primeMS[#]<Total[primeMS[#]]&]

CROSSREFS

The enumeration of these partitions by sum is A327781.

Heinz numbers of partitions whose LCM is twice their sum are A327775.

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, A316413, A326841, A327779.

Sequence in context: A110615 A060679 A051234 * A102554 A070810 A227180

Adjacent sequences:  A327773 A327774 A327775 * A327777 A327778 A327779

KEYWORD

nonn

AUTHOR

Gus Wiseman, Sep 25 2019

STATUS

approved

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Last modified June 14 15:19 EDT 2021. Contains 345025 sequences. (Running on oeis4.)