A388980 Even numbers of the form p * m^2, where p is prime and m > 0.

2, 8, 12, 18, 20, 28, 32, 44, 48, 50, 52, 68, 72, 76, 80, 92, 98, 108, 112, 116, 124, 128, 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, 512

Offset

1,1

Comments

Even numbers k such that A007913(k) is a prime.

Links

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

Maple

M:= 1000: # for terms <= M
P:= select(isprime, {seq(i, i=3..M/4, 2)}):
R:= {seq(2*m^2, m=1..floor(sqrt(M/2)))} union map(proc(p) local m; seq(p*m^2, m=2..floor(sqrt(M/p)), 2) end proc, P):
sort(convert(R, list)); # Robert Israel, Sep 25 2025

Prog

(PARI) is_A388980(k) = (!(k%2) && isprime(core(k)));
(PARI)
up_to = 16384;
A388980list(up_to) = { my(v=vector(up_to), i=0); forstep(n=2, oo, 2, if(isprime(core(n)), i++; v[i] = n; if(i==up_to, return(v)))); };
v388980 = A388980list(up_to);
A388980(n) = v388980[n];
(Python)
from math import isqrt
from sympy import primepi
from oeis_sequences.OEISsequences import bisection
def A388980(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))
    return bisection(f, n, n) # Chai Wah Wu, Sep 22 2025
(Python)
from sympy import isprime
from sympy.ntheory.factor_ import core
def is_A388980(k): return (k%2 == 0 and isprime(core(k))) # Robert C. Lyons, Sep 25 2025

Crossrefs

Even terms of A229125. After the initial 2 also the even terms of A228056.

The topmost row of A388982.

Cf. A007913.

Sequence in context: A340690 A303900 A046470 * A090772 A046525 A235353

Adjacent sequences: A388977 A388978 A388979 * A388981 A388982 A388983

Keyword

nonn

Author

Antti Karttunen, Sep 22 2025

Status

approved