OFFSET
1,1
COMMENTS
f(n>=1) =1, 1, 2, 4, 4, 2, 6, 10, 10, 4, 10, 8, 12, 6, 8, 22, 16, 10, 18, 16, 12...
EXAMPLE
f(200) = f(2^3*5^2) = (-2+2^2+2^3)*(-2+5+5^2) = 280.
f(880) = 880.
Factorizations: 2^2, 2^3*5, 2^4*5*11, 2^5*5*11*23, 2^6*5*11*23*47, 2^10*3^2*5*7*13*29*59.
MAPLE
f := proc(n)
local a, p, e ;
a := 1 ;
for d in ifactors(n)[2] do
p := op(1, d) ;
e := op(2, d) ;
a := a* (p^(e-1)+p^e-2) ;
end do:
a ;
end proc:
for n from 1 do
if n = f(n) then
print(n) ;
end if;
end do: # R. J. Mathar, Mar 13 2024
MATHEMATICA
f[p_, e_] := p^e + p^(e - 1) - 2; s[n_] := Times @@ f @@@ FactorInteger[n]; s[1] = 0; Select[Range[4*10^6], s[#] == # &] (* Amiram Eldar, Aug 26 2022 *)
CROSSREFS
KEYWORD
nonn,more
AUTHOR
EXTENSIONS
Offset corrected by Amiram Eldar, Aug 26 2022
STATUS
approved