A395381 a(1) = 12; for n > 1, a(n) is the number of integers k from [prime(n-1)^9..prime(n)^9 - 1] with exactly 10 divisors.

12, 254, 14555, 220397, 10251887, 32883544, 386214098, 686526363, 4665218030, 37045468979, 33464687016, 277535584514, 509216235683, 442678008025, 1525098385911, 5228913860475, 12469865414304, 6929152649967, 34817529046730, 41065452601877, 28387924629796

Offset

1,1

Links

Chai Wah Wu, Table of n, a(n) for n = 1..132

Example

a(1) = 12 because [1..511] contains 12 numbers 48, 80, 112, 162, 176, 208, 272, 304, 368, 405, 464, 496 with exactly 10 divisors;
a(2) = 254 because [512..19682] contains 254 numbers 512, 567, 592, 676, ..., 19664 with exactly 10 divisors;
a(3) = 14555 because [19683..1953124] contains 14555 numbers 19683, 19696, 19792, ..., 1953104 with exactly 10 divisors.

Prog

(Magma) [12] cat [#[k: k in [NthPrime(n-1)^9..NthPrime(n)^9-1] | #Divisors(k) eq 10]: n in [2..3]];
(Python)
from sympy import prime, primepi, primerange, integer_nthroot
def A395381(n):
    if n == 1: return 12
    def f(x):
        p = prime(x)**9
        return sum(primepi(p//k**4) for k in primerange(integer_nthroot(p, 4)[0]+1))-primepi(integer_nthroot(p, 5)[0])
    return 1+f(n)-f(n-1) # Chai Wah Wu, Apr 21 2026

Crossrefs

Cf. A000005, A030628 (without 1), A179665, A390951.

Sequence in context: A129585 A034672 A133285 * A239778 A113091 A053324

Adjacent sequences: A395378 A395379 A395380 * A395382 A395383 A395384

Keyword

nonn

Author

Juri-Stepan Gerasimov, Apr 20 2026

Extensions

a(4)-a(21) from Chai Wah Wu, Apr 21 2026

Status

approved