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

Author

Amiram Eldar, Jun 09 2017

Keywords

• nonn

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

Examples

			The iterated phi of 25 are 20, 8, 4, 2, 1 and 25 = 20 + 4 + 1.
		

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..10000

Crossrefs

Supersequence of A082897. Subsequence of A286265.

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

Programs

Mathematica

pseudoPerfectTotQ[n_]:= Module[{tots = Most[Rest[FixedPointList[EulerPhi@# &, n]]]}, MemberQ[Total /@ Subsets[tots, Length[tots]], n]]; Select[Range[155], pseudoPerfectTotQ]

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