A319151 Heinz numbers of superperiodic integer partitions.

2, 3, 5, 7, 9, 11, 13, 17, 19, 23, 25, 27, 29, 31, 37, 41, 43, 47, 49, 53, 59, 61, 67, 71, 73, 79, 81, 83, 89, 97, 101, 103, 107, 109, 113, 121, 125, 127, 131, 137, 139, 149, 151, 157, 163, 167, 169, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233

Offset

1,1

Comments

First differs from A061345 at a(1) = 2 and next at a(98) = 441.

A number n is in the sequence iff n = 2 or the prime indices of n have a common divisor > 1 and the Heinz number of the multiset of prime multiplicities of n, namely A181819(n), is already in the sequence.

The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..2326

Example

The sequence of partitions whose Heinz numbers belong to the sequence begins: (1), (2), (3), (4), (2,2), (5), (6), (7), (8), (9), (3,3), (2,2,2), (10), (11), (12), (13), (14), (15), (4,4), (16), (17), (18), (19), (20), (21), (22), (2,2,2,2).

Mathematica

supperQ[n_]:=Or[n==2, And[GCD@@PrimePi/@FactorInteger[n][[All, 1]]>1, supperQ[Times@@Prime/@FactorInteger[n][[All, 2]]]]];
Select[Range[500], supperQ]

Crossrefs

Cf. A001597, A056239, A072774, A098859, A181819, A182850, A289509, A296150, A298748, A304464, A305732, A317246, A317257, A319149, A319152, A319157.

Sequence in context: A329559 A305081 A235868 * A180934 A090332 A325395

Adjacent sequences: A319148 A319149 A319150 * A319152 A319153 A319154

Keyword

nonn

Author

Gus Wiseman, Sep 12 2018

Status

approved