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

5, 9, 11, 13, 17, 19, 21, 23, 25, 27, 29, 33, 34, 35, 37, 38, 39, 41, 43, 45, 47, 49, 50, 51, 53, 55, 57, 59, 61, 65, 67, 68, 69, 71, 73, 74, 75, 76, 77, 79, 81, 83, 85, 86, 87, 89, 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

Offset: 1

Author

Eric Chen, Sep 13 2021

Keywords

• nonn

Comments

Numbers not appearing in A047994.

Indices of -1 in A135347.

Unitary version of A007617.

This sequence to A047994 is A007617 to A000010.

This sequence to A135347 is A007617 to A049283 (for the case that no such numbers exist, A135347 uses -1 and A049283 uses 0).

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.

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.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000010, A002202, A005277, A007617, A047994, A049225, A049283, A135347, A361966, A361967.

Programs

Mathematica

Select[Range[135], Length[invUPhi[#]] == 0 &] (* Amiram Eldar, Apr 01 2023, using the function invUPhi from A361966 *)

PARI

A047994(n)=my(f=factor(n)~); prod(i=1, #f, f[1, i]^f[2, i]-1)
is(n)=for(k=1,n^2,if(A047994(k)==n,return(0)));1 \\ after A047994

Formula

A361967(a(n)) = 0. - Amiram Eldar, Apr 01 2023