A325500 Heinz number of the set of Heinz numbers of integer partitions of n. Heinz numbers of rows of A215366.

2, 3, 35, 2717, 22235779, 3163570326979, 51747966790650260753033, 188828800892079861898153036258130093, 2034903808706825942766196978067005215014684343665351270467, 75367279796373180679613801327275978589820813788234346991420766634058571423774287454563

Offset

0,1

Comments

The Heinz number of a set of positive integers {y_1,...,y_k} is prime(y_1)*...*prime(y_k).

All terms are squarefree and pairwise relatively prime.

Links

Table of n, a(n) for n=0..9.

Index entries for sequences related to Heinz numbers

Formula

A001221(a(n)) = A001222(a(n)) = A000041(n).

A056239(a(n)) = A145519(n).

A003963(a(n)) = A325501(n).

A181819(A003963(a(n))) = A325507(n).

Example

The integer partitions of 3 are {(3), (2,1), (1,1,1)}, with Heinz numbers {5,6,8}, with Heinz number prime(5)*prime(6)*prime(8) = 2717, so a(3) = 2717.
The sequence of terms together with their prime indices begins:
                        2: {1}
                        3: {2}
                       35: {3,4}
                     2717: {5,6,8}
                 22235779: {7,9,10,12,16}
            3163570326979: {11,14,15,18,20,24,32}
  51747966790650260753033: {13,21,22,25,27,28,30,36,40,48,64}

Mathematica

Table[Times@@Prime/@(Times@@Prime/@#&/@IntegerPartitions[n]), {n, 0, 5}]

Crossrefs

A subsequence of A005117.

Cf. A001222, A002110, A003963, A006128, A007870, A056239, A066186, A066633, A112798, A145519, A215366, A325501, A325505, A325507.

Sequence in context: A111459 A042663 A072291 * A084191 A080357 A064032

Adjacent sequences: A325497 A325498 A325499 * A325501 A325502 A325503

Keyword

nonn

Author

Gus Wiseman, May 05 2019

Status

approved