A063668 -id:A063668 - cp's OEIS frontend

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

Franz Vrabec, Aug 05 2019

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)

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

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.

Cf. A002202, A016825, A114874.

Supersequence of A063668.

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

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

A071624 Numbers k such that phi(m) = 96*k+2 has no solution.

Original entry on oeis.org

0, 378, 1524, 2385, 7749, 13788, 21555, 34599, 46398, 50715, 59925, 69903, 75180, 86310, 104445, 117495, 177375, 230349, 239850, 269505, 290235, 311733, 380835, 393024, 470190, 497448, 525474, 583830, 598899, 743160, 760149, 812268, 902973, 998478, 1018155

Offset: 1

Labos Elemer, May 29 2002

nonn

Cf. A063667, A063668, A000010, A005277, A002202.

Maple
```
[seq(nops(invphi(2+96*i)),i=1..25000)];
```

s=0; m=96; r=2; Do[s=EulerPhi[n]; If[Equal[Mod[s, m], r], Print[(s-r)/m]], {n, 1, 100000000}]

a(20)-a(35) from Donovan Johnson, Jul 27 2011

cp's OEIS Frontend

A309502 Totients congruent to 2 mod 4.

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