A394226 a(1) = 4; for n > 1, a(n) is the number of integers k from [prime(n-1)^5..prime(n)^5 - 1] with exactly 6 divisors where prime(n) = n-th prime.

4, 27, 251, 908, 7387, 9449, 42221, 39528, 138840, 454766, 250398, 1201227, 1315046, 860814, 2227899, 4949209, 7528262, 3228855, 12360603, 10884568, 6372164, 23452759, 19814016, 37234487, 66650343, 42039006, 23501193, 52437822, 29137840, 64622169, 304995118

Offset

1,1

Links

Chai Wah Wu, Table of n, a(n) for n = 1..190

Example

a(1) = 4; for n > 1 because [1..31] contains 4 numbers 12, 18, 20, 28 with exactly 6 divisors;
a(2) = 27 because [32..242] contains 27 numbers 32, 44, 45, ..., 242 with exactly 6 divisors;
a(3) = 251 because [243..3124] contains 251 numbers 243, 244, 245, ..., 3124 with exactly 6 divisors.

Prog

(Magma) [4] cat [#[k: k in [NthPrime(n-1)^5..NthPrime(n)^5-1] | #Divisors(k) eq 6]: n in [2..9]];
(PARI) a(n) = if (n==1, 4, #select(x->numdiv(x)==6, [prime(n-1)^5..prime(n)^5 - 1])); \\ Michel Marcus, Apr 15 2026
(Python)
from math import isqrt
from sympy import prime, primepi, primerange, integer_nthroot
def A394226(n):
    if n == 1: return 4
    def f(x):
        p = prime(x)**5
        return sum(primepi(p//k**2) for k in primerange(isqrt(p)+1))-primepi(integer_nthroot(p, 3)[0])
    return 1+f(n)-f(n-1) # Chai Wah Wu, Apr 21 2026

Crossrefs

Cf. A030515, A393179, A394917.

Sequence in context: A239369 A246526 A273994 * A239378 A239376 A239373

Adjacent sequences: A394223 A394224 A394225 * A394227 A394228 A394229

Keyword

nonn,more

Author

Juri-Stepan Gerasimov, Apr 14 2026

Extensions

a(12)-a(16) from Michel Marcus, Apr 15 2026

a(17)-a(31) from Chai Wah Wu, Apr 21 2026

Status

approved