

A317257


Heinz numbers of totally nonincreasing integer partitions.


6



1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 51, 52, 53, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70
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OFFSET

1,2


COMMENTS

The first term absent from this sequence but present in A242031 is 180.
A positive integer n belongs to the sequence if either n is 1 or prime or has weakly decreasing prime multiplicities (so it belongs to A242031) and A181819(n) already belongs to the sequence.
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..67.


MATHEMATICA

primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
totincQ[q_]:=Or[Length[q]<=1, And[OrderedQ[Length/@Split[q]], totincQ[Reverse[Length/@Split[q]]]]];
Select[Range[100], totincQ[Reverse[primeMS[#]]]&]


CROSSREFS

Cf. A056239, A100883, A181819, A182850, A242031, A296150, A305732, A317246, A317256, A317258.
Sequence in context: A076084 A151764 A093618 * A242031 A109427 A249830
Adjacent sequences: A317254 A317255 A317256 * A317258 A317259 A317260


KEYWORD

nonn


AUTHOR

Gus Wiseman, Jul 25 2018


STATUS

approved



