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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. 4
 1, 2, 4, 6, 8, 12, 16, 18, 20, 24 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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 From Jianing Song, Dec 12 2021: (Start) Conjecture: defining this sequence as "positive integers m such that whenever n > 1 is in the range of the Euler totient function, so is m*n" would give the same terms. That is to say, it seems that if m is a nontotient number, then there exists a totient number n > 1 such that m*n is a nontotient. The known primitive terms of this sequence (terms that are not products of two previous terms) are 1, 2, 6, 18, 20. More terms are needed to determine the primitive terms further. (End) LINKS EXAMPLE 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. CROSSREFS Sequence in context: A015937 A058825 A087086 * A319796 A103288 A125225 Adjacent sequences:  A301584 A301585 A301586 * A301588 A301589 A301590 KEYWORD nonn,more AUTHOR David L. Harden, Mar 24 2018 STATUS approved

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Last modified July 3 05:07 EDT 2022. Contains 355030 sequences. (Running on oeis4.)