A336016 a(n) is the number of primes q less than primorial(n) having k = 2 as the least exponent such that q^k == 1 (mod primorial(n)).

0, 1, 3, 5, 8, 19, 22, 51, 89, 145, 263, 453, 851, 1575, 2880, 5469, 10338, 19115, 35782, 67569, 128601, 243600, 463840, 883589

Offset: 1

Author

Michael De Vlieger, David James Sycamore, David A. Corneth, Jul 10 2020

Keywords

• nonn
• more

Comments

a(n) = length of row n of A336015 for n > 1.

Examples

			a(4) = 5 as there are 5 primes q coprime to primorial(4) = 210 such that 2 is the least positive integer exponent k where q^k == 1 (mod 210). Those primes are 29, 41, 71, 139, 181 and indeed we have 29^2 == 1 (mod 210), 41^2 == 1 (mod 210), 71^2 == 1 (mod 210), 139^2 == 1 (mod 210) and 181^2 == 1 (mod 210) and no more below 210. So as these are five such primes in row 4, a(4) = 5. - _David A. Corneth_, Aug 15 2020
		

Crossrefs

Cf. A000010, A002110, A005867, A131577, A336015.

Programs

Mathematica

Table[Block[{P = #, k = 0}, Do[If[MultiplicativeOrder[Prime@ i, P] == 2, k++], {i, PrimePi[n + 1], PrimePi[P - 1]}]; k] &@ Product[Prime@ j, {j, n}], {n, 8}]

PARI

a(n) = {if(n <= 2, return(n-1)); my(pp = vecprod(primes(n))/2, d = divisors(pp), res = 0); for(i = 1, #d, c = lift(chinese(Mod(-1, d[i]), Mod(1, pp/d[i]))); forstep(i = c, pp*2, pp, if(isprime(i), res++ ) ) ); res } \\ David A. Corneth, Aug 16 2020

Extensions

New name from David A. Corneth, Aug 15 2020