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A345988
Smallest oblong number m*(m+1) that is divisible by n.
3
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.
MATHEMATICA
Module[{nn=60, ob}, ob=Table[m(m+1), {m, nn}]; Table[SelectFirst[ob, Mod[#, n]==0&], {n, nn}]] (* Harvey P. Dale, Jul 10 2024 *)
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
Sequence in context: A361426 A157285 A320068 * A275439 A173392 A324128
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jul 13 2021
STATUS
approved