A395380 a(1) = 4; for n > 1, a(n) is the number of integers k in [prime(n-1)^8..prime(n)^8 - 1] with exactly 9 divisors.

4, 19, 160, 483, 3089, 3328, 12563, 10379, 32184, 88507, 43668, 188210, 184134, 113384, 276419, 559933, 772460, 312726, 1129061, 932029, 525311, 1842227, 1471593, 2621705, 4372435, 2610735, 1421029, 3089490, 1675216, 3621466, 15889018, 5569261, 9318716, 3378641

Offset

1,1

Links

Chai Wah Wu, Table of n, a(n) for n = 1..412

Example

a(1) = 4 because [1..255] contains 4 numbers 36, 100, 196, 225 with exactly 9 divisors;
a(2) = 19 because [256..6560] contains 19 numbers 256, 441, 484, 676, 1089, 1156, 12225, 1444, 1521, 2116, 2601, 3025, 3249, 3364, 3844, 4225, 4761, 5476, 5929 with exactly 9 divisors;
a(3) = 160 because [6561..390624] contains 160 numbers 6561, 6524, 7225, ..., 388129 with exactly 9 divisors.

Prog

(Magma) [4] cat [#[k: k in [NthPrime(n-1)^8..NthPrime(n)^8-1] | #Divisors(k) eq 9]: n in [2..4]];
(Python)
from math import comb
from sympy import prime, primepi, primerange
def A395380(n):
    if n == 1: return 4
    def f(x):
        s = prime(x)**2
        y = s**2
        return int(-(t:=primepi(s))-comb(t, 2)+sum(primepi(y//k) for k in primerange(1, s+1)))
    return 1+f(n)-f(n-1) # Chai Wah Wu, Apr 23 2026

Crossrefs

Cf. A000005, A030627, A179645, A390951, A394226.

Sequence in context: A225904 A203010 A362380 * A249785 A341379 A155804

Adjacent sequences: A395377 A395378 A395379 * A395381 A395382 A395383

Keyword

nonn

Author

Juri-Stepan Gerasimov, Apr 20 2026

Extensions

a(5)-a(34) from Chai Wah Wu, Apr 23 2026

Status

approved