%I
%S 11,17,21,23,27,31,50,55,56,65,71,89,129,131,144,155,169,204,209,216,
%T 229,239,241,244,251,265,287,288,300,305,337,344,351,371,373,379,407,
%U 415,493,494,517,526,545,577,645,647,664,681,685,737,749,755,769,776,780,783,815
%N Numbers whose neighbor's prime factors with multiplicity can be partitioned into two multisets of equal sum.
%C The neighbors of n are the two numbers n1 and n+1.
%H Jonathan Frech, <a href="/A325902/b325902.txt">Table of n, a(n) for n = 1..10000</a>
%e 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.
%t 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 *)
%o (Haskell)
%o import Data.List (subsequences, (\\))
%o factors 1 = []
%o factors n  p < head $ filter ((== 0) . mod n) [2..]
%o = p : factors (n `div` p)
%o sumPartitionable ns  p < \ms > sum ms == sum (ns \\ ms)
%o = any p $ subsequences ns
%o a325902 = filter (\n > sumPartitionable $ factors (n1) ++ factors (n+1)) [2..]
%Y Cf. A063968.
%K nonn
%O 1,1
%A _Jonathan Frech_, Sep 07 2019
