A369108 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.
2, 15, 123, 1074, 9623, 87882, 814183, 7618317, 71838469, 681591775, 6499182987
Offset: 1
Links
- Gareth A. Jones and Alexander K. Zvonkin, A number-theoretic problem concerning pseudo-real Riemann surfaces, arXiv:2401.00270 [math.NT], 2023. See Table 2 at page 7.
Programs
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Mathematica
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] -
PARI
is1(n) = n % 4 == 1 && factorback(factor(n)[, 1] % 4) == 1 \\ Charles R Greathouse IV at A004613 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
Extensions
a(10)-a(11) from Amiram Eldar, Jun 03 2024