A395381 - OEIS

%I #31 May 22 2026 22:12:38

%S 12,254,14555,220397,10251887,32883544,386214098,686526363,4665218030,

%T 37045468979,33464687016,277535584514,509216235683,442678008025,

%U 1525098385911,5228913860475,12469865414304,6929152649967,34817529046730,41065452601877,28387924629796

%N 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.

%H Chai Wah Wu, <a href="/A395381/b395381.txt">Table of n, a(n) for n = 1..132</a>

%e 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;

%e a(2) = 254 because [512..19682] contains 254 numbers 512, 567, 592, 676, ..., 19664 with exactly 10 divisors;

%e a(3) = 14555 because [19683..1953124] contains 14555 numbers 19683, 19696, 19792, ..., 1953104 with exactly 10 divisors.

%o (Magma) [12] cat [#[k: k in [NthPrime(n-1)^9..NthPrime(n)^9-1] | #Divisors(k) eq 10]: n in [2..3]];

%o (Python)

%o from sympy import prime, primepi, primerange, integer_nthroot

%o def A395381(n):

%o     if n == 1: return 12

%o     def f(x):

%o         p = prime(x)**9

%o         return sum(primepi(p//k**4) for k in primerange(integer_nthroot(p,4)[0]+1))-primepi(integer_nthroot(p,5)[0])

%o     return 1+f(n)-f(n-1) # _Chai Wah Wu_, Apr 21 2026

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

%K nonn

%O 1,1

%A _Juri-Stepan Gerasimov_, Apr 20 2026

%E a(4)-a(21) from _Chai Wah Wu_, Apr 21 2026