A325902 Numbers whose neighbor's prime factors with multiplicity can be partitioned into two multisets of equal sum.

11, 17, 21, 23, 27, 31, 50, 55, 56, 65, 71, 89, 129, 131, 144, 155, 169, 204, 209, 216, 229, 239, 241, 244, 251, 265, 287, 288, 300, 305, 337, 344, 351, 371, 373, 379, 407, 415, 493, 494, 517, 526, 545, 577, 645, 647, 664, 681, 685, 737, 749, 755, 769, 776, 780, 783, 815

Offset

1,1

Comments

The neighbors of n are the two numbers n-1 and n+1.

Links

Jonathan Frech, Table of n, a(n) for n = 1..10000

Example

71 is in the sequence since 70 = 2*5*7 < 71 < 2*2*2*3*3 = 72 with 2 + 5 + 3 + 3 = 7 + 2 + 2 + 2.

Mathematica

ok[n_] := Block[{t, p, m, z}, {p, m} = Transpose@ Tally@ Sort[ Join@ Flatten[ ConstantArray @@@ FactorInteger[#] & /@ {n-1, n+1}]]; t = Total[p m]; If[ OddQ@ t, False, z = Quiet@ LinearProgramming[1 + 0 p, {p}, {{t/2, 0}}, Prepend[#, 0] & /@ Transpose@{m}, Integers]; ListQ@z && Total[z p]==t/2]]; Select[ Range[3, 815], ok] (* Giovanni Resta, Sep 10 2019 *)

Prog

(Haskell)
import Data.List (subsequences, (\\))
factors 1 = []
factors n | p <- head $ filter ((== 0) . mod n) [2..]
          = p : factors (n `div` p)
sumPartitionable ns | p <- \ms -> sum ms == sum (ns \\ ms)
                    = any p $ subsequences ns
a325902 = filter (\n -> sumPartitionable $ factors (n-1) ++ factors (n+1)) [2..]

Crossrefs

Cf. A063968.

Sequence in context: A362083 A322476 A176603 * A050715 A006618 A184551

Adjacent sequences: A325899 A325900 A325901 * A325903 A325904 A325905

Keyword

nonn

Author

Jonathan Frech, Sep 07 2019

Status

approved