cp's OEIS Frontend

A309502 Totients congruent to 2 mod 4.

%I A309502 #38 Dec 13 2024 10:25:12
%S A309502 2,6,10,18,22,30,42,46,54,58,66,70,78,82,102,106,110,126,130,138,150,
%T A309502 162,166,178,190,198,210,222,226,238,250,262,270,282,294,306,310,330,
%U A309502 342,346,358,366,378,382,418,430,438,442,462,466,478,486,490,498,502
%N A309502 Totients congruent to 2 mod 4.
%C A309502 Intersection of A002202 and A016825.
%C A309502 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.
%C A309502 From _Jianing Song_, Aug 23 2021: (Start)
%C A309502 Numbers of the form (p-1)*p^e for primes p == 3 (mod 4), e >= 0.
%C A309502 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)
%H A309502 Amiram Eldar, <a href="/A309502/b309502.txt">Table of n, a(n) for n = 1..10000</a>
%H A309502 Andre Contiero and Davi Lima, <a href="https://arxiv.org/abs/1803.01396">On the distribution of totients 2 mod. 4</a>, arXiv:1803.01396 [math.NT], 4 Mar 2018.
%H A309502 André Contiero and Davi Lima, <a href="https://arxiv.org/abs/2005.05475">2-Adic Stratification of Totients</a>, arXiv:2005.05475 [math.NT], 2020.
%H A309502 V. L. Klee, Jr., <a href="https://www.jstor.org/stable/2305504">On the equation phi(x)=2m</a>, Amer. Math. Monthly, 53 (1946), 327.
%e A309502 10 = phi(11) = phi(22) and 10 == 2 (mod 4), so 10 is in the sequence.
%o A309502 (PARI) isok(t) = istotient(t) && ((t % 4) == 2); \\ _Michel Marcus_, Aug 05 2019
%Y A309502 Cf. A002202, A016825, A114874.
%Y A309502 Supersequence of A063668.
%K A309502 nonn,easy
%O A309502 1,1
%A A309502 _Franz Vrabec_, Aug 05 2019
%E A309502 New name using existing comment from _Michel Marcus_, May 14 2020