OFFSET
1,1
COMMENTS
Analogous to A005835 (pseudoperfect numbers) as A082897 (perfect totient numbers) is analogous to A000396 (perfect numbers).
All the odd primes are in this sequence.
Number of terms < 10^k: 4, 40, 350, 2956, 24842, etc. - Robert G. Wilson v, Jun 17 2017
All terms are odd. If n is even, phi(n) <= n/2, and except for n = 2, we will have phi(n) also even. So the sum of the phi sequence < n*(1/2 + 1/4 + ...) = n. - Franklin T. Adams-Watters, Jun 25 2017
LINKS
Robert G. Wilson v, Table of n, a(n) for n = 1..10000
EXAMPLE
The iterated phi of 25 are 20, 8, 4, 2, 1 and 25 = 20 + 4 + 1.
MATHEMATICA
pseudoPerfectTotQ[n_]:= Module[{tots = Most[Rest[FixedPointList[EulerPhi@# &, n]]]}, MemberQ[Total /@ Subsets[tots, Length[tots]], n]]; Select[Range[155], pseudoPerfectTotQ]
PROG
(PARI) subsetSum(v, target)=if(setsearch(v, target), return(1)); if(#v<2, return(target==0)); my(u=v[1..#v-1]); if(target>v[#v] && subsetSum(u, target-v[#v]), return(1)); subsetSum(u, target);
is(n)=if(isprime(n), return(n>2)); my(v=List(), k=n); while(k>1, listput(v, k=eulerphi(k))); subsetSum(Set(v), n) \\ Charles R Greathouse IV, Jun 25 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Jun 09 2017
STATUS
approved