A316438 Heinz numbers of integer partitions whose product is strictly greater than the LCM of the parts.

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

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: A254066 A015785 A366290 * A208135 A306382 A373351

Adjacent sequences: A316435 A316436 A316437 * A316439 A316440 A316441

Keyword

nonn

Author

Gus Wiseman, Jul 03 2018

Status

approved