A394226 - OEIS

%I #24 Apr 22 2026 00:55:21

%S 4,27,251,908,7387,9449,42221,39528,138840,454766,250398,1201227,

%T 1315046,860814,2227899,4949209,7528262,3228855,12360603,10884568,

%U 6372164,23452759,19814016,37234487,66650343,42039006,23501193,52437822,29137840,64622169,304995118

%N 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.

%H Chai Wah Wu, <a href="/A394226/b394226.txt">Table of n, a(n) for n = 1..190</a>

%e a(1) = 4; for n > 1 because [1..31] contains 4 numbers 12, 18, 20, 28 with exactly 6 divisors;

%e a(2) = 27 because [32..242] contains 27 numbers 32, 44, 45, ..., 242 with exactly 6 divisors;

%e a(3) = 251 because [243..3124] contains 251 numbers 243, 244, 245, ..., 3124 with exactly 6 divisors.

%o (Magma) [4] cat [#[k: k in [NthPrime(n-1)^5..NthPrime(n)^5-1] | #Divisors(k) eq 6]: n in [2..9]];

%o (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

%o (Python)

%o from math import isqrt

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

%o def A394226(n):

%o     if n == 1: return 4

%o     def f(x):

%o         p = prime(x)**5

%o         return sum(primepi(p//k**2) for k in primerange(isqrt(p)+1))-primepi(integer_nthroot(p,3)[0])

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

%Y Cf. A030515, A393179, A394917.

%K nonn,more

%O 1,1

%A _Juri-Stepan Gerasimov_, Apr 14 2026

%E a(12)-a(16) from _Michel Marcus_, Apr 15 2026

%E a(17)-a(31) from _Chai Wah Wu_, Apr 21 2026