A135347 An inverse of the unitary totient function A047994.

1, 3, 4, 5, -1, 7, 8, 9, -1, 11, -1, 13, -1, 24, 16, 17, -1, 19, -1, 33, -1, 23, -1, 25, -1, 27, -1, 29, -1, 31, 32, 45, -1, -1, -1, 37, -1, -1, -1, 41, -1, 43, -1, 69, -1, 47, -1, 49, -1, -1, -1, 53, -1, 76, -1, 72, -1, 59, -1, 61, -1, 96, 64, 85, -1, 67, -1, -1, -1, 71, -1, 73, -1, -1, -1, -1, -1, 79, -1, 81, -1, 83, -1, 104, -1, -1, -1

Offset: 1

Author

R. J. Mathar, Dec 07 2007

Keywords

• sign

Comments

a(n) is the smallest m such that A047994(m)=n, or -1 if this m does not exist. Proof of nonexistence may be done by transversing all A045778(n) factorizations of n, increasing each factor in these factorizations by 1 and showing that none of these modified products is a product of powers of distinct primes.

Links

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

Crossrefs

Cf. A047994, A045778, A361966.

Programs

Mathematica

a[n_] := Module[{v = invUPhi[n]}, If[v == {}, -1, v[[1]]]]; Array[a, 100] (* Amiram Eldar, Apr 01 2023, using the function invUPhi from A361966 *)