OFFSET
1,1
COMMENTS
Let the multiplicity of a(n) be the number of m such that phi(m)=a(n), a(1)=2 has multiplicity 3 (phi(3)=phi(4)=phi(6)=2) and all other terms have multiplicity 2 or 4.
From Jianing Song, Aug 23 2021: (Start)
Numbers of the form (p-1)*p^e for primes p == 3 (mod 4), e >= 0.
The terms with multiplicity 4 are the numbers in A114874 that are congruent to 2 modulo 4 and greater than 2, that is, the numbers of the form k = (p-1)*p^e for primes p == 3 (mod 4), e >= 1, where k+1 is prime. In this case, the numbers m such that phi(m) = k are m = k+1, 2*(k+1), p^(e+1) and 2*p^(e+1). (End)
LINKS
Andre Contiero, and Davi Lima, On the distribution of totients 2 mod. 4, arXiv:1803.01396 [math.NT], 4 Mar 2018.
André Contiero, and Davi Lima, 2-Adic Stratification of Totients, arXiv:2005.05475 [math.NT], 2020.
V. L. Klee, Jr., On the equation phi(x)=2m, Amer. Math. Monthly, 53 (1946), 327.
EXAMPLE
10 = phi(11) = phi(22) and 10 == 2 (mod 4), so 10 is in the sequence.
PROG
(PARI) isok(t) = istotient(t) && ((t % 4) == 2); \\ Michel Marcus, Aug 05 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Franz Vrabec, Aug 05 2019
EXTENSIONS
New name using existing comment from Michel Marcus, May 14 2020
STATUS
approved