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A096290
Prime power perfect numbers: If n = Product p_i^r_i let PPsigma(n) = Product {Sum p_i^s_i, 2<=s_i<=r_i, s_i is prime}; sequence gives numbers k such that PPsigma(k) = 2*k.
6
216, 5400, 10584, 26136, 36504, 62424, 77976, 114264, 181656, 207576, 264600, 295704, 363096, 399384, 477144, 606744, 653400, 751896, 803736, 912600, 969624, 1088856, 1149984, 1151064, 1280664, 1348056, 1488024, 1560600, 1710936, 1788696, 1949400, 2032344, 2203416
OFFSET
1,1
LINKS
EXAMPLE
5400 is in the sequence because 5400 = 2^3*3^3*5^2 and (2^2+2^3)*(3^2+3^3)*(5^2) = 2*5400.
MAPLE
PPsigma := proc(n)
option remember;
local a, pe, p, e, f, i ;
a := 1 ;
for pe in ifactors(n)[2] do
p := op(1, pe) ;
e := op(2, pe) ;
f := 0 ;
for i from 2 to e do
if isprime(i) then
f := f+p^i ;
end if;
end do:
a := a*f ;
end do;
a ;
end proc:
for n from 1 do
if PPsigma(n) = 2*n then
print(n) ;
end if;
end do: # R. J. Mathar, Mar 13 2024
MATHEMATICA
f[p_, e_] := Plus @@ (p^Select[Range[e], PrimeQ]); s[n_] := Times @@ f @@@ FactorInteger[n]; Select[Range[300000], s[#] == 2*# &] (* Amiram Eldar, Sep 19 2022 *)
CROSSREFS
Cf. A100509.
Sequence in context: A183617 A114060 A128964 * A246896 A017595 A232835
KEYWORD
nonn
AUTHOR
Yasutoshi Kohmoto, Jun 24 2004
EXTENSIONS
Corrected and extended by Farideh Firoozbakht, Nov 17 2004
More terms from Amiram Eldar, Sep 19 2022
STATUS
approved