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

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 30, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 154, 157, 163, 165, 167, 173, 179, 181, 190, 191, 193, 197, 198, 199, 211, 223, 227, 229, 233, 239, 241

Offset

1,1

Comments

First differs from A319333 in having 154.

First nonsquarefree term is 198.

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..58.

Formula

A056239(a(k)) | A290103(a(k)).

Example

The sequence of terms together with their prime indices begins:
    2: {1}
    3: {2}
    5: {3}
    7: {4}
   11: {5}
   13: {6}
   17: {7}
   19: {8}
   23: {9}
   29: {10}
   30: {1,2,3}
   31: {11}
   37: {12}
   41: {13}
   43: {14}
   47: {15}
   53: {16}
   59: {17}
   61: {18}
   67: {19}

Mathematica

primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[2, 100], Divisible[LCM@@primeMS[#], Total[primeMS[#]]]&]

Crossrefs

The enumeration of these partitions by sum is A327778.

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

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

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

Cf. A056239, A074761, A112798, A290103, A316413, A326841, A327779.

Sequence in context: A365829 A030059 A201879 * A319333 A326715 A338925

Adjacent sequences: A327780 A327781 A327782 * A327784 A327785 A327786

Keyword

nonn

Author

Gus Wiseman, Sep 25 2019

Status

approved