cp's OEIS Frontend

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

%I A288452 #18 Jun 25 2017 15:13:57
%S A288452 3,5,7,9,11,13,15,17,19,23,25,27,29,31,33,35,37,39,41,43,47,49,51,53,
%T A288452 55,59,61,65,67,69,71,73,77,79,81,83,85,87,89,97,101,103,107,109,111,
%U A288452 113,115,119,121,123,125,127,131,137,139,141,143,149,151,153,155
%N A288452 Pseudoperfect totient numbers: numbers n such that equal the sum of a subset of their iterated phi(n).
%C A288452 Analogous to A005835 (pseudoperfect numbers) as A082897 (perfect totient numbers) is analogous to A000396 (perfect numbers).
%C A288452 All the odd primes are in this sequence.
%C A288452 Number of terms < 10^k: 4, 40, 350, 2956, 24842, etc. - _Robert G. Wilson v_, Jun 17 2017
%C A288452 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
%H A288452 Robert G. Wilson v, <a href="/A288452/b288452.txt">Table of n, a(n) for n = 1..10000</a>
%e A288452 The iterated phi of 25 are 20, 8, 4, 2, 1 and 25 = 20 + 4 + 1.
%t A288452 pseudoPerfectTotQ[n_]:= Module[{tots = Most[Rest[FixedPointList[EulerPhi@# &, n]]]}, MemberQ[Total /@ Subsets[tots, Length[tots]], n]]; Select[Range[155], pseudoPerfectTotQ]
%o A288452 (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);
%o A288452 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
%Y A288452 Supersequence of A082897. Subsequence of A286265.
%Y A288452 Cf. A000010, A000396, A005835, A053478, A092693.
%K A288452 nonn
%O A288452 1,1
%A A288452 _Amiram Eldar_, Jun 09 2017