A339907 - OEIS

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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

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OFFSET

1,1

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.

PROG

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

CROSSREFS

Cf. A339906.

Cf. A065091, A339908 (subsequences).

Cf. also A339817.

Apart from initial 3, a subsequence of A339910.

Sequence in context: A351398 A285516 A319801 * A255602 A319181 A318718

Adjacent sequences: A339904 A339905 A339906 * A339908 A339909 A339910

KEYWORD

nonn

AUTHOR

Antti Karttunen, Dec 21 2020

STATUS

approved