A388984 Even numbers, not powers of primes, that are of the form p * m^2, where p is prime and m by necessity > 1.

12, 18, 20, 28, 44, 48, 50, 52, 68, 72, 76, 80, 92, 98, 108, 112, 116, 124, 148, 162, 164, 172, 176, 180, 188, 192, 200, 208, 212, 236, 242, 244, 252, 268, 272, 284, 288, 292, 300, 304, 316, 320, 332, 338, 356, 368, 388, 392, 396, 404, 412, 428, 432, 436, 448, 450, 452, 464, 468, 496, 500, 508, 524, 548, 556, 578

Offset

1,1

Comments

Even numbers k of the form p * m^2, where p is prime and A001221(k) > 1.

Even terms k of A024619 such that A007913(k) is a prime.

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Prog

(PARI) is_A388984(k) = (!(k%2) && !isprimepower(k) && isprime(core(k)));
(PARI) is_A388984(k) = (!(k%2) && isprime(core(k)) && omega(k)>1);
(PARI)
up_to = 10000;
A388984list(up_to) = { my(v=vector(up_to), i=0); forstep(n=2, oo, 2, if(isprime(core(n)) && !isprimepower(n), i++; v[i] = n; if(i==up_to, return(v)))); };
v388984 = A388984list(up_to);
A388984(n) = v388984[n];
(Python)
from math import isqrt
from sympy import primepi
from oeis_sequences.OEISsequences import bisection
def A388984(n):
    def f(x): return n+x-(isqrt(x>>1)+1>>1)-sum(primepi(x//y**2) for y in range(2, isqrt(x)+1, 2))+(x.bit_length()>>1)
    return bisection(f, n, n) # Chai Wah Wu, Sep 25 2025

Crossrefs

Even terms of A388983.

Sequence A388980 without any powers of 2 (A000079).

Cf. A001221, A007913, A024619.

The top row of A388981.

Sequence in context: A072357 A340780 A054753 * A098899 A098770 A381546

Adjacent sequences: A388981 A388982 A388983 * A388985 A388986 A388987

Keyword

nonn

Author

Antti Karttunen, Sep 22 2025

Status

approved