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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
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
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
KEYWORD
nonn
AUTHOR
Michel Lagneau, Mar 09 2015
EXTENSIONS
a(7)-a(24) from Hiroaki Yamanouchi, Mar 26 2015
STATUS
approved