A288452 Pseudoperfect totient numbers: numbers n such that equal the sum of a subset of their iterated phi(n).

3, 5, 7, 9, 11, 13, 15, 17, 19, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 47, 49, 51, 53, 55, 59, 61, 65, 67, 69, 71, 73, 77, 79, 81, 83, 85, 87, 89, 97, 101, 103, 107, 109, 111, 113, 115, 119, 121, 123, 125, 127, 131, 137, 139, 141, 143, 149, 151, 153, 155

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

Supersequence of A082897. Subsequence of A286265.

Cf. A000010, A000396, A005835, A053478, A092693.

Sequence in context: A143452 A376342 A372293 * A338316 A193414 A138217

Adjacent sequences: A288449 A288450 A288451 * A288453 A288454 A288455

Keyword

nonn

Author

Amiram Eldar, Jun 09 2017

Status

approved