A345444 a(n) = A344005(2*n+1).

1, 2, 4, 6, 8, 10, 12, 5, 16, 18, 6, 22, 24, 26, 28, 30, 11, 14, 36, 12, 40, 42, 9, 46, 48, 17, 52, 10, 18, 58, 60, 27, 25, 66, 23, 70, 72, 24, 21, 78, 80, 82, 34, 29, 88, 13, 30, 19, 96, 44, 100, 102, 14, 106, 108, 36, 112, 45, 26, 34, 120, 41, 124, 126, 42, 130, 56, 54, 136, 138, 47, 65, 29

Offset

0,2

Comments

The companion bisection to A011772.

Links

Table of n, a(n) for n=0..72.

Formula

a(n) = 2*n if 2*n+1 is a prime power. - Chai Wah Wu, Jul 06 2021

Prog

(Python 3.8+)
from itertools import combinations
from math import prod
from sympy import factorint, divisors
from sympy.ntheory.modular import crt
def A345444(n):
    if n == 0:
        return 1
    k = 2*n+1
    plist = [p**q for p, q in factorint(k).items()]
    return k-1 if len(plist) == 1 else int(min(min(crt([m, k//m], [0, -1])[0], crt([k//m, m], [0, -1])[0]) for m in (prod(d) for l in range(1, len(plist)//2+1) for d in combinations(plist, l)))) # Chai Wah Wu, Jul 06 2021

Crossrefs

Cf. A011772, A344005.

Sequence in context: A241071 A353026 A356431 * A319807 A055954 A366021

Adjacent sequences: A345441 A345442 A345443 * A345445 A345446 A345447

Keyword

nonn

Author

N. J. A. Sloane, Jul 06 2021

Status

approved