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A316438 Heinz numbers of integer partitions whose product is strictly greater than the LCM of the parts. 3
9, 18, 21, 25, 27, 36, 39, 42, 45, 49, 50, 54, 57, 63, 65, 72, 75, 78, 81, 84, 87, 90, 91, 98, 99, 100, 105, 108, 111, 114, 115, 117, 121, 125, 126, 129, 130, 133, 135, 144, 147, 150, 153, 156, 159, 162, 168, 169, 171, 174, 175, 180, 182, 183, 185, 189, 195 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Also numbers n > 1 such that A290104(n) > 1.

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..57.

EXAMPLE

Sequence of partitions whose product is greater than their LCM begins: (22), (221), (42), (33), (222), (2211), (62), (421), (322), (44), (331), (2221), (82), (422), (63), (22111), (332), (621), (2222), (4211).

MATHEMATICA

Select[Range[2, 300], With[{pms=Flatten[Cases[FactorInteger[#], {p_, k_}:>Table[PrimePi[p], {k}]]]}, Times@@pms/LCM@@pms>1]&]

CROSSREFS

Cf. A056239, A074761, A143773, A285572, A289508, A290103, A296150, A316429, A316431, A316433, A316437.

Sequence in context: A062057 A254066 A015785 * A208135 A306382 A222623

Adjacent sequences:  A316435 A316436 A316437 * A316439 A316440 A316441

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jul 03 2018

STATUS

approved

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Last modified September 21 14:54 EDT 2020. Contains 337272 sequences. (Running on oeis4.)