A309502 Totients congruent to 2 mod 4.

2, 6, 10, 18, 22, 30, 42, 46, 54, 58, 66, 70, 78, 82, 102, 106, 110, 126, 130, 138, 150, 162, 166, 178, 190, 198, 210, 222, 226, 238, 250, 262, 270, 282, 294, 306, 310, 330, 342, 346, 358, 366, 378, 382, 418, 430, 438, 442, 462, 466, 478, 486, 490, 498, 502

Offset: 1

Author

Franz Vrabec, Aug 05 2019

Keywords

• nonn
• easy

Comments

Intersection of A002202 and A016825.

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)

Examples

			10 = phi(11) = phi(22) and 10 == 2 (mod 4), so 10 is in the sequence.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• 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.

Crossrefs

Cf. A002202, A016825, A114874.

Supersequence of A063668.

Programs

PARI

isok(t) = istotient(t) && ((t % 4) == 2); \\ Michel Marcus, Aug 05 2019

Extensions

New name using existing comment from Michel Marcus, May 14 2020