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A322657 Integers whose set of divisors, excluding 1, can be partitioned into two nonempty subsets having equal sum. 1
36, 72, 144, 200, 288, 324, 392, 400, 450, 576, 648, 784, 800, 882, 900, 1152, 1296, 1568, 1600, 1764, 1800, 1936, 2178, 2304, 2450, 2592, 2704, 2916, 3042, 3136, 3200, 3528, 3600, 3872, 4050, 4356, 4608, 4900, 5000, 5184, 5202, 5408, 5832, 6050, 6084, 6272, 6400, 6498 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Called two-layered numbers in Behzadipour link.

LINKS

Table of n, a(n) for n=1..48.

Hussein Behzadipour, Two-layered numbers, arXiv:1812.07233 [math.NT], 2018.

EXAMPLE

36 is a term with {2, 3, 4, 36} and {6, 9, 12, 18} having equal sums 45.

MAPLE

a:= proc(n) option remember; local k, l, t, b; b:=

      proc(m, i) option remember; m=0 or i>0 and

        (b(m, i-1) or l[i]<=m and b(m-l[i], i-1)) end;

      for k from 1+`if`(n=1, 1, a(n-1)) do

        l:= sort([(numtheory[divisors](k) minus {1})[]]);

        t:= add(i, i=l);

        if t::even then forget(b);

          if b(t/2, nops(l)) then return k fi

        fi

      od

    end:

seq(a(n), n=1..50);  # Alois P. Heinz, Dec 22 2018

MATHEMATICA

aQ[n_] := Module[{d = Rest[Divisors[n]], t, ds, x}, ds = Plus @@ d; If[Mod[ds, 2] > 0, False, t = CoefficientList[Product[1 + x^i, {i, d}], x]; t[[1 + ds/2]] > 0]]; Select[Range[2, 6500], aQ] (* Amiram Eldar, Dec 22 2018 after T. D. Noe at A083207 *)

PROG

(PARI) part(n, v)=if(n<1, return(n==0)); forstep(i=#v, 2, -1, if(part(n-v[i], v[1..i-1]), return(1))); n==v[1];

is(n)=my(d=divisors(n), dd = select(x->(x>1), d), s=sum(i=1, #dd, dd[i])); s%2==0 && part(s/2-n, dd[1..#dd-1]); \\ both after pari in A083207

CROSSREFS

Cf. A083207, A322658.

Sequence in context: A031479 A153642 A119843 * A066216 A032497 A024973

Adjacent sequences:  A322654 A322655 A322656 * A322658 A322659 A322660

KEYWORD

nonn

AUTHOR

Michel Marcus, Dec 22 2018

STATUS

approved

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Last modified February 17 15:19 EST 2019. Contains 320220 sequences. (Running on oeis4.)