A339907 Odd squarefree numbers k > 1 for which the bigomega(phi(k)) <= bigomega(k-1), where bigomega gives the number of prime divisors, counted with multiplicity.

3, 5, 7, 11, 13, 17, 19, 21, 23, 29, 31, 33, 37, 41, 43, 47, 53, 55, 57, 59, 61, 65, 67, 69, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 129, 131, 137, 139, 141, 145, 149, 151, 157, 161, 163, 167, 173, 177, 179, 181, 191, 193, 197, 199, 201, 209, 211, 217, 223, 227, 229, 233, 235, 239, 241, 249, 251, 253, 257

Offset: 1

Author

Antti Karttunen, Dec 21 2020

Keywords

• nonn

Comments

Terms of A003961(A019565(A339906(i))) [or equally, of A019565(2*A339906(i))], for i = 1.., sorted into ascending order.

Natural numbers n > 2 that satisfy equation k * phi(n) = n - 1 (for some integer k) all occur in this sequence. Lehmer conjectured that there are no composite solutions.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..18526
• D. H. Lehmer, On Euler's totient function, Bulletin of the American Mathematical Society, 38 (1932), 745-751.
• Wikipedia, Lehmer's totient problem.

Crossrefs

Cf. A339906.

Cf. A065091, A339908 (subsequences).

Cf. also A339817.

Apart from initial 3, a subsequence of A339910.

Programs

PARI

isA339907(n) = ((n>1)&&(n%2)&&issquarefree(n)&&(bigomega(eulerphi(n))<=bigomega(n-1)));