

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
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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. AdamsWatters, 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..#v1]); if(target>v[#v] && subsetSum(u, targetv[#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



