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