A055128 Fixed points of the following function: if n = Product p(i)^r(i) then f(n) = Product (-2+p(i)^(r(i)-1)+p(i)^r(i)).

4, 40, 880, 40480, 3805120, 7174702080

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...

Links

Table of n, a(n) for n=1..6.

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

Sequence in context: A325293 A121276 A013053 * A117251 A220404 A211040

Adjacent sequences: A055125 A055126 A055127 * A055129 A055130 A055131

Keyword

nonn,more

Author

Yasutoshi Kohmoto

Extensions

Offset corrected by Amiram Eldar, Aug 26 2022

Status

approved