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a(n) is the number of numbers less than or equal to 10^n that are divisible only by primes congruent to 1 mod 4.
4

%I #13 Jun 03 2024 03:48:20

%S 2,15,123,1074,9623,87882,814183,7618317,71838469,681591775,6499182987

%N a(n) is the number of numbers less than or equal to 10^n that are divisible only by primes congruent to 1 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 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[1, {m,PrimeNu[#]}] && #<=10^n &]]]; Array[a, 9]

%o (PARI) is1(n) = n % 4 == 1 && factorback(factor(n)[, 1] % 4) == 1 \\ _Charles R Greathouse IV_ at A004613

%o lista(nmax) = {my(c = 0, pow = 10, n = 1, nm = nmax + 1); for(k = 1, 10^nmax + 1, if(k > pow, print1(c, ", "); pow *= 10; n++; if(n == nm, break)); if(is1(k), c++));} \\ _Amiram Eldar_, Jun 03 2024

%Y Cf. A004613, A369105, A369107, A369109, A369111.

%K nonn,more

%O 1,1

%A _Stefano Spezia_, Jan 13 2024

%E a(10)-a(11) from _Amiram Eldar_, Jun 03 2024