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

%I A325902 #25 Sep 10 2019 23:34:01
%S A325902 11,17,21,23,27,31,50,55,56,65,71,89,129,131,144,155,169,204,209,216,
%T A325902 229,239,241,244,251,265,287,288,300,305,337,344,351,371,373,379,407,
%U A325902 415,493,494,517,526,545,577,645,647,664,681,685,737,749,755,769,776,780,783,815
%N A325902 Numbers whose neighbor's prime factors with multiplicity can be partitioned into two multisets of equal sum.
%C A325902 The neighbors of n are the two numbers n-1 and n+1.
%H A325902 Jonathan Frech, <a href="/A325902/b325902.txt">Table of n, a(n) for n = 1..10000</a>
%e A325902 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 A325902 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 *)
%o A325902 (Haskell)
%o A325902 import Data.List (subsequences, (\\))
%o A325902 factors 1 = []
%o A325902 factors n | p <- head $ filter ((== 0) . mod n) [2..]
%o A325902           = p : factors (n `div` p)
%o A325902 sumPartitionable ns | p <- \ms -> sum ms == sum (ns \\ ms)
%o A325902                     = any p $ subsequences ns
%o A325902 a325902 = filter (\n -> sumPartitionable $ factors (n-1) ++ factors (n+1)) [2..]
%Y A325902 Cf. A063968.
%K A325902 nonn
%O A325902 1,1
%A A325902 _Jonathan Frech_, Sep 07 2019