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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. 1
2, 4, 240, 348, 368, 380, 19364665320, 20210069880, 20328267960, 20673770040, 20681420760, 20735165880, 20940748920, 20959618680, 21135474360, 21196014840, 21256222680, 21302746920, 21380630040, 21405023640, 21426252120, 21465896760, 21522002040, 21544621560 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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

LINKS

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

EXAMPLE

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

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 *)

PROG

(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

CROSSREFS

Cf. A000593, A146076, A245015.

Sequence in context: A018729 A009800 A018742 * A018747 A110067 A145996

Adjacent sequences:  A255888 A255889 A255890 * A255892 A255893 A255894

KEYWORD

nonn

AUTHOR

Michel Lagneau, Mar 09 2015

EXTENSIONS

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

STATUS

approved

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Last modified January 18 16:40 EST 2019. Contains 319271 sequences. (Running on oeis4.)