|
%I #14 Jun 03 2024 03:48:26
%S 4,26,201,1680,14902,135124,1243370,11587149,108941388,1031330156,
%T 9816605847
%N a(n) is the number of numbers less than or equal to 10^n that are divisible only by primes congruent to 3 mod 4.
%H Gareth A. Jones and Alexander K. Zvonkin, <a href="https://arxiv.org/abs/2401.00270">A number-theoretic problem concerning pseudo-real Riemann surfaces</a>, arXiv:2401.00270 [math.NT], 2023. See Table 1 at page 6 and Table 2 at page 7.
%t a[n_] := Length[Join[{1}, Select[Range[10^n], PrimeQ[f = First/@FactorInteger[#]] == Table[True, {j,PrimeNu[#]}] && Mod[f,4] == Table[3, {m,PrimeNu[#]}] && #<=10^n &]]]; Array[a, 10]
%o (PARI) is1(n) = {my(p = factor(n)[, 1]); for(i = 1, #p, if(p[i] % 4 == 1, return(0))); 1;};
%o lista(nmax) = {my(c = 0, pow = 10, n = 1, nm = nmax + 1); forstep(k = 1, 10^nmax + 1, 2, if(k > pow, print1(c, ", "); pow *= 10; n++; if(n == nm, break)); if(is1(k), c++));} \\ _Amiram Eldar_, Jun 03 2024
%Y Cf. A004614, A004767, A011557, A369105, A369108, A369109, A369111.
%K nonn,more
%O 1,1
%A _Stefano Spezia_, Jan 13 2024
%E a(11) from _Amiram Eldar_, Jun 03 2024
|
