A369107 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.

4, 26, 201, 1680, 14902, 135124, 1243370, 11587149, 108941388, 1031330156, 9816605847

Offset

1,1

Links

Table of n, a(n) for n=1..11.

Gareth A. Jones and Alexander K. Zvonkin, A number-theoretic problem concerning pseudo-real Riemann surfaces, arXiv:2401.00270 [math.NT], 2023. See Table 1 at page 6 and Table 2 at page 7.

Mathematica

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]

Prog

(PARI) is1(n) = {my(p = factor(n)[, 1]); for(i = 1, #p, if(p[i] % 4 == 1, return(0))); 1; };
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

Crossrefs

Cf. A004614, A004767, A011557, A369105, A369108, A369109, A369111.

Sequence in context: A192499 A271935 A246509 * A368976 A253255 A141381

Adjacent sequences: A369104 A369105 A369106 * A369108 A369109 A369110

Keyword

nonn,more

Author

Stefano Spezia, Jan 13 2024

Extensions

a(11) from Amiram Eldar, Jun 03 2024

Status

approved