A345988 Smallest oblong number m*(m+1) that is divisible by n.

2, 2, 6, 12, 20, 6, 42, 56, 72, 20, 110, 12, 156, 42, 30, 240, 272, 72, 342, 20, 42, 110, 506, 72, 600, 156, 702, 56, 812, 30, 930, 992, 132, 272, 210, 72, 1332, 342, 156, 240, 1640, 42, 1806, 132, 90, 506, 2162, 240, 2352, 600, 306, 156, 2756, 702, 110, 56, 342, 812, 3422, 240

Offset

1,1

Comments

Equals A344005(n)*(A344005(n)+1). See A344005 for much more about this problem.

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Prog

(Python 3.8+)
from itertools import combinations
from math import prod
from sympy import factorint
from sympy.ntheory.modular import crt
def A345988(n):
    if n == 1:
        return 2
    plist = tuple(p**q for p, q in factorint(n).items())
    return n*(n-1) if len(plist) == 1 else (s:= int(min(min(crt((m, n//m), (0, -1))[0], crt((n//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)))))*(s+1) # Chai Wah Wu, May 31 2022

Crossrefs

Cf. A002378, A344005.

Sequence in context: A361426 A157285 A320068 * A275439 A173392 A324128

Adjacent sequences: A345985 A345986 A345987 * A345989 A345990 A345991

Keyword

nonn

Author

N. J. A. Sloane, Jul 13 2021

Status

approved