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A317258 Heinz numbers of integer partitions that are not totally nonincreasing. 5
18, 50, 54, 75, 90, 98, 108, 126, 147, 150, 162, 180, 198, 234, 242, 245, 250, 252, 270, 294, 300, 306, 324, 338, 342, 350, 363, 375, 378, 396, 414, 450, 468, 486, 490, 500, 507, 522, 525, 540, 550, 558, 578, 588, 594, 600, 605, 612, 630, 648, 650, 666, 684 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

An integer partition is totally nonincreasing if either it is empty or a singleton or its multiplicities (where if x < y the multiplicity of x is counted prior to the multiplicity of y) are weakly decreasing and are themselves a totally nonincreasing integer partition.

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..53.

EXAMPLE

Sequence of all integer partitions that are not totally nonincreasing begins: (221), (331), (2221), (332), (3221), (441), (22211), (4221), (442), (3321), (22221), (32211), (5221), (6221), (551), (443), (3331), (42211), (32221), (4421), (33211), (7221), (222211), (661), (8221), (4331), (552), (3332), (42221), (52211), (9221), (33221).

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[1000], !totincQ[Reverse[primeMS[#]]]&]

CROSSREFS

Cf. A056239, A071365, A100883, A112769, A181819, A182850, A242031, A296150, A305733, A317256, A317257.

Sequence in context: A178398 A222740 A335377 * A071365 A097319 A258211

Adjacent sequences:  A317255 A317256 A317257 * A317259 A317260 A317261

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jul 25 2018

STATUS

approved

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Last modified May 23 13:45 EDT 2022. Contains 353975 sequences. (Running on oeis4.)