This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
Number 24 is in the sequence because sigma(14) = sigma(15) = sigma(23) = 24.
240 is in the sequence because A000593(240)= 24 = 4! and A146076(240)= 720 = 6!
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:
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 *)
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
sigma(14) = 24 = tau(14)! = 4!.
[m: m in [1..5*10^6] | &+Divisors(m) eq Factorial(#Divisors(m))];
Select[Range[40000], DivisorSigma[1, #] == DivisorSigma[0, #]! &] (* Amiram Eldar, Feb 22 2022 *)
isok(m) = my(f=factor(m)); sigma(f) == numdiv(f)!; \\ Michel Marcus, Feb 23 2022
Comments