A278568 Twice odd prime powers.

2, 6, 10, 14, 18, 22, 26, 34, 38, 46, 50, 54, 58, 62, 74, 82, 86, 94, 98, 106, 118, 122, 134, 142, 146, 158, 162, 166, 178, 194, 202, 206, 214, 218, 226, 242, 250, 254, 262, 274, 278, 298, 302, 314, 326, 334, 338, 346, 358, 362, 382, 386, 394, 398, 422, 446, 454, 458, 466, 478

Offset

1,1

Links

Table of n, a(n) for n=1..60.

L. J. Corwin, Irreducible polynomials over the integers which factor mod p for every p, Unpublished Bell Labs Memo, Sep 07 1967 [Annotated scanned copy]

Prog

(Python)
from sympy import primepi, integer_nthroot
def A278568(n):
    def bisection(f, kmin=0, kmax=1):
        while f(kmax) > kmax: kmax <<= 1
        kmin = kmax >> 1
        while kmax-kmin > 1:
            kmid = kmax+kmin>>1
            if f(kmid) <= kmid:
                kmax = kmid
            else:
                kmin = kmid
        return kmax
    def f(x): return int(n+x-1-sum(primepi(integer_nthroot(x, k)[0])-1 for k in range(1, x.bit_length())))
    return bisection(f, n, n)<<1 # Chai Wah Wu, Feb 03 2025

Crossrefs

Twice A061345.

Sequence in context: A333662 A290490 A182991 * A250198 A260084 A194282

Adjacent sequences: A278565 A278566 A278567 * A278569 A278570 A278571

Keyword

nonn

Author

N. J. A. Sloane, Nov 26 2016

Status

approved