

A325902


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


1



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
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OFFSET

1,1


COMMENTS

The neighbors of n are the two numbers n1 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[#] & /@ {n1, 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 (n1) ++ factors (n+1)) [2..]


CROSSREFS

Cf. A063968.
Sequence in context: A050669 A322476 A176603 * A050715 A006618 A184551
Adjacent sequences: A325899 A325900 A325901 * A325903 A325904 A325905


KEYWORD

nonn


AUTHOR

Jonathan Frech, Sep 07 2019


STATUS

approved



