A336435 a(n) is the least k such that A069230(k) = n.

1, 3, 2, 4, 14, 6, 16, 63, 20, 18, 12, 64, 102, 66, 24, 40, 100, 208, 112, 36, 650, 444, 200, 198, 228, 160, 84, 72, 96, 60, 1610, 320, 1110, 192, 1218, 324, 400, 728, 462, 144, 280, 264, 270, 168, 120, 882, 828, 468, 980, 588, 288, 252, 300, 1040, 1104, 180, 880

Offset: 0

Author

David A. Corneth, Sep 20 2020

Keywords

• nonn

Examples

			a(10) = 12 as A069230(12) = 10 as there are 10 primes between (exclusive) 12 and 12 + tau(12)^2 = 12 + 6^2 = 12 + 36 = 48 namely the 10 primes 13, 17, 19, 23, 29, 31, 37, 41, 43, 47 and k = 12 is the least k such that there are ten primes between (exclusive) k and k + tau(k)^2 where tau is the number of divisors (Cf. A000005).
		

Links

• Amiram Eldar, Table of n, a(n) for n = 0..2500

Crossrefs

Cf. A000005, A069230.

Programs

PARI

A069230(n) = {my(cnt = 0); for(k = n+1, n+numdiv(n)^2-1, cnt += isprime(k)); cnt;};
list(nmax) = {my(v = vector(nmax+1), c = 0, k = 1, i); while(c < nmax+1, i = A069230(k) + 1; if(i <= nmax + 1 && v[i] == 0, c++; v[i] = k); k++); v;} \\ Amiram Eldar, Jan 29 2025