A255891 Numbers n such that the sum of the even divisors of n is equal to m! and the sum of the odd divisors of n is equal to k! for some integers m and k.

2, 4, 240, 348, 368, 380, 19364665320, 20210069880, 20328267960, 20673770040, 20681420760, 20735165880, 20940748920, 20959618680, 21135474360, 21196014840, 21256222680, 21302746920, 21380630040, 21405023640, 21426252120, 21465896760, 21522002040, 21544621560

Offset: 1

Author

Michel Lagneau, Mar 09 2015

Keywords

• nonn

Comments

Numbers n such that A000593(n) = m! and A146076(n) = k! for some m and k.

Is this sequence finite? No further terms less than 10^6.

No further terms less than 10^9. - Michel Marcus, Mar 10 2015

sigma(a(25711)) >= 29! + 30!. - Hiroaki Yamanouchi, Mar 26 2015

Examples

			240 is in the sequence because A000593(240)= 24 = 4! and A146076(240)= 720 = 6!
		

Links

• Hiroaki Yamanouchi, Table of n, a(n) for n = 1..25710

Crossrefs

Cf. A000593, A146076, A245015.

Programs

Maple

for n from 2 by 2  to 20000 do:
   y:=divisors(n):n1:=nops(y):s0:=0:s1:=0:
     for k from 1 to n1 do:
       if irem(y[k],2)=0
        then
        s0:=s0+ y[k]:
        else
        s1:=s1+ y[k]:
      fi:
     od:
     ii:=0:
        for a from 1 to 20 while(ii=0)do:
         if s0=a!
          then
           for b from 1 to 20 while(ii=0) do:
             if s1=b!
              then
              ii:=1:print(n):
              else
             fi:
           od:
          fi:
        od:
      od:

Mathematica

fQ[n_] := Block[{d = Divisors@ n, lst = Array[Factorial, {449}]}, MemberQ[lst, Plus @@ Select[d, EvenQ]] && MemberQ[lst, Plus @@ Select[d, OddQ]]]; Select[Range@10000, fQ] (* Michael De Vlieger, Mar 10 2015 *)

PARI

isoks(s) = {if (s==1, return (1)); f = 1; for (k=2, s, f *= k; if (f == s, return (1)); if (f > s, return (0)););}
isok(n) = my(sod = sumdiv(n, d, d*(d%2))); my(sed = sigma(n) - sod); sod && sed && isoks(sed) && isoks(sod); \\ Michel Marcus, Mar 10 2015

Extensions

a(7)-a(24) from Hiroaki Yamanouchi, Mar 26 2015