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 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

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