A301970 Heinz numbers of integer partitions with more subset-products than subset-sums.

165, 273, 325, 351, 495, 525, 561, 595, 675, 741, 765, 819, 825, 931, 1045, 1053, 1155, 1173, 1425, 1485, 1495, 1575, 1625, 1653, 1683, 1771, 1785, 1815, 1911, 2025, 2139, 2145, 2223, 2275, 2277, 2295, 2310, 2415, 2457, 2465, 2475, 2625, 2639, 2695, 2805, 2945

Offset

1,1

Comments

The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k). A subset-sum (or subset-product) of a multiset y is any number equal to the sum (or product) of some submultiset of y.

Numbers n such that A301957(n) > A299701(n).

Links

Table of n, a(n) for n=1..46.

Example

Sequence of partitions begins: (532), (642), (633), (6222), (5322), (4332), (752), (743), (33222), (862), (7322), (6422), (5332), (844), (853), (62222), (5432), (972), (8332), (53222), (963), (43322), (6333).

Mathematica

Select[Range[1000], With[{ptn=If[#===1, {}, Join@@Cases[FactorInteger[#], {p_, k_}:>Table[PrimePi[p], {k}]]]}, Length[Union[Times@@@Subsets[ptn]]]>Length[Union[Plus@@@Subsets[ptn]]]]&]

Crossrefs

Cf. A000712, A003963, A056239, A108917, A276024, A284640, A292886, A296150, A299701, A299702, A299729, A301854, A301855, A301856, A301957, A301979.

Sequence in context: A319502 A270175 A319328 * A176877 A356095 A323379

Adjacent sequences: A301967 A301968 A301969 * A301971 A301972 A301973

Keyword

nonn

Author

Gus Wiseman, Mar 29 2018

Status

approved