login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A288452 Pseudoperfect totient numbers: numbers n such that equal the sum of a subset of their iterated phi(n). 3
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 (list; graph; refs; listen; history; text; internal format)
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: A093031 A305468 A143452 * A193414 A138217 A074775

Adjacent sequences:  A288449 A288450 A288451 * A288453 A288454 A288455

KEYWORD

nonn

AUTHOR

Amiram Eldar, Jun 09 2017

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 13 01:23 EST 2019. Contains 329963 sequences. (Running on oeis4.)