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A301587 Positive integers m such that whenever n is in the range of the Euler totient function, so is m*n. 1
1, 2, 4, 6, 8, 12, 16, 18, 20, 24 (list; graph; refs; listen; history; text; internal format)



Closure under multiplication: if multiplication by m_1 carries totient values to totient values and multiplication by m_2 does also, then so does their composition, which is multiplication by m_1*m_2.

No odd terms are in the sequence except for 1.

32, 36, 40, 42, 48, 54, 64, and 72 are also in this sequence, although determining their position is difficult. - Charlie Neder, Aug 04 2019


Table of n, a(n) for n=1..10.


1 is trivially in the sequence.

Note that any value assumed by phi is assumed at an even argument, since k odd implies phi(k) = phi(2k).

Then 2 is in the sequence, since n = phi(k) and k even imply that 2n = phi(2k).

3 is not in the sequence: 30 = phi(31), but 90 is not in the range of phi.

4 is in the sequence because 2 is (using closure under multiplication).

5 is not in the sequence: 18 = phi(19), but 90 is not in the range of phi.

6 is in the sequence: If n = phi(k) with k even, phi(9k) = 6n if k is a nonmultiple of 3. If k is a multiple of 3, then 6n = phi(6k) since k is a multiple of 6.

7 is not in the sequence: 22 = phi(23), but 154 is not in the range of phi.

8 is in the sequence because 2 is.


Sequence in context: A015937 A058825 A087086 * A319796 A103288 A125225

Adjacent sequences:  A301584 A301585 A301586 * A301588 A301589 A301590




David L. Harden, Mar 24 2018



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Last modified May 9 22:17 EDT 2021. Contains 343746 sequences. (Running on oeis4.)