cp's OEIS Frontend

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.

%I A255891 #23 Mar 26 2015 17:19:05
%S A255891 2,4,240,348,368,380,19364665320,20210069880,20328267960,20673770040,
%T A255891 20681420760,20735165880,20940748920,20959618680,21135474360,
%U A255891 21196014840,21256222680,21302746920,21380630040,21405023640,21426252120,21465896760,21522002040,21544621560
%N 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.
%C A255891 Numbers n such that A000593(n) = m! and A146076(n) = k! for some m and k.
%C A255891 Is this sequence finite? No further terms less than 10^6.
%C A255891 No further terms less than 10^9. - _Michel Marcus_, Mar 10 2015
%C A255891 sigma(a(25711)) >= 29! + 30!. - _Hiroaki Yamanouchi_, Mar 26 2015
%H A255891 Hiroaki Yamanouchi, <a href="/A255891/b255891.txt">Table of n, a(n) for n = 1..25710</a>
%e A255891 240 is in the sequence because A000593(240)= 24 = 4! and A146076(240)= 720 = 6!
%p A255891 for n from 2 by 2  to 20000 do:
%p A255891    y:=divisors(n):n1:=nops(y):s0:=0:s1:=0:
%p A255891      for k from 1 to n1 do:
%p A255891        if irem(y[k],2)=0
%p A255891         then
%p A255891         s0:=s0+ y[k]:
%p A255891         else
%p A255891         s1:=s1+ y[k]:
%p A255891       fi:
%p A255891      od:
%p A255891      ii:=0:
%p A255891         for a from 1 to 20 while(ii=0)do:
%p A255891          if s0=a!
%p A255891           then
%p A255891            for b from 1 to 20 while(ii=0) do:
%p A255891              if s1=b!
%p A255891               then
%p A255891               ii:=1:print(n):
%p A255891               else
%p A255891              fi:
%p A255891            od:
%p A255891           fi:
%p A255891         od:
%p A255891       od:
%t A255891 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 *)
%o A255891 (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)););}
%o A255891 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
%Y A255891 Cf. A000593, A146076, A245015.
%K A255891 nonn
%O A255891 1,1
%A A255891 _Michel Lagneau_, Mar 09 2015
%E A255891 a(7)-a(24) from _Hiroaki Yamanouchi_, Mar 26 2015