cp's OEIS Frontend

A347771 Unitary nontotient numbers: values not in range of unitary totient function uphi(n).

%I A347771 #34 Apr 01 2023 22:05:55
%S A347771 5,9,11,13,17,19,21,23,25,27,29,33,34,35,37,38,39,41,43,45,47,49,50,
%T A347771 51,53,55,57,59,61,65,67,68,69,71,73,74,75,76,77,79,81,83,85,86,87,89,
%U A347771 91,93,94,95,97,98,99,101,103,105,107,109,110,111,113,114,115,117,118,119,121,122,123,125,129,131,133,134,135
%N A347771 Unitary nontotient numbers: values not in range of unitary totient function uphi(n).
%C A347771 Numbers not appearing in A047994.
%C A347771 Indices of -1 in A135347.
%C A347771 Unitary version of A007617.
%C A347771 This sequence to A047994 is A007617 to A000010.
%C A347771 This sequence to A135347 is A007617 to A049283 (for the case that no such numbers exist, A135347 uses -1 and A049283 uses 0).
%C A347771 All odd numbers not of the form 2^k-1 (i.e. not in A000225) are in this sequence, since uphi(n) = A047994(n) is an even number unless n is a power of 2 (A000079), in this case uphi(n) = n-1.
%C A347771 The intersection of this sequence and A049225 is empty, since for squarefree numbers, all divisors are unitary divisors, note that the intersection of this sequence and A002202 is not empty, the number 110 is in both sequences.
%H A347771 Amiram Eldar, <a href="/A347771/b347771.txt">Table of n, a(n) for n = 1..10000</a>
%F A347771 A361967(a(n)) = 0. - _Amiram Eldar_, Apr 01 2023
%t A347771 Select[Range[135], Length[invUPhi[#]] == 0 &] (* _Amiram Eldar_, Apr 01 2023, using the function invUPhi from A361966 *)
%o A347771 (PARI) A047994(n)=my(f=factor(n)~); prod(i=1, #f, f[1, i]^f[2, i]-1)
%o A347771 is(n)=for(k=1,n^2,if(A047994(k)==n,return(0)));1 \\ after A047994
%Y A347771 Cf. A000010, A002202, A005277, A007617, A047994, A049225, A049283, A135347, A361966, A361967.
%K A347771 nonn
%O A347771 1,1
%A A347771 _Eric Chen_, Sep 13 2021