A319329 Heinz numbers of integer partitions whose length is equal to the GCD of the parts and whose sum is equal to the LCM of the parts.

2, 1495, 179417, 231133, 727531

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..5.

Example

The sequence of partitions whose length is equal to their GCD and whose sum is equal to their LCM begins: (1), (9,6,3), (20,8,8,4), (24,16,4,4), (16,16,12,4).

Mathematica

Select[Range[2, 10000], With[{m=If[#==1, {}, Flatten[Cases[FactorInteger[#], {p_, k_}:>Table[PrimePi[p], {k}]]]]}, And[LCM@@m==Total[m], GCD@@m==Length[m]]]&]

Crossrefs

Cf. A056239, A067538, A074761, A143773, A289508, A289509, A290103, A290104, A316430, A316431, A316432, A319328, A319330, A319333.

Sequence in context: A172234 A339543 A023291 * A058423 A233906 A329775

Adjacent sequences: A319326 A319327 A319328 * A319330 A319331 A319332

Keyword

nonn,more

Author

Gus Wiseman, Sep 17 2018

Status

approved