A345994 - OEIS

A345994

Let m = A344005(n) = smallest m such that n divides m*(m+1); a(n) = min(gcd(n,m), gcd(n,m+1)).

1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 3, 1, 2, 3, 1, 1, 2, 1, 4, 3, 2, 1, 3, 1, 2, 1, 4, 1, 5, 1, 1, 3, 2, 5, 4, 1, 2, 3, 5, 1, 6, 1, 4, 5, 2, 1, 3, 1, 2, 3, 4, 1, 2, 5, 7, 3, 2, 1, 4, 1, 2, 7, 1, 5, 6, 1, 4, 3, 5, 1, 8, 1, 2, 3, 4, 7, 6, 1, 5, 1, 2, 1, 4, 5, 2, 3, 8, 1, 9, 7, 4, 3, 2, 5

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OFFSET

1,6

COMMENTS

This is the minimum of A345992 and A345993.

LINKS

N. J. A. Sloane, Table of n, a(n) for n = 1..10000

PROG

(Python 3.8+)

from math import gcd, prod

from itertools import combinations

from sympy import factorint

from sympy.ntheory.modular import crt

def A345994(n):

if n == 1:

return 1

plist = tuple(p**q for p, q in factorint(n).items())

return 1 if len(plist) == 1 else min(gcd(n, 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))))), gcd(n, s+1)) # Chai Wah Wu, Jun 17 2022

CROSSREFS

Cf. A344005, A345992, A345993, A345995, A346956.

Cf. also A051119, A284600.

Sequence in context: A284556 A025865 A085091 * A052128 A284600 A114536

Adjacent sequences: A345991 A345992 A345993 * A345995 A345996 A345997

KEYWORD

nonn

AUTHOR

Robert Dougherty-Bliss and N. J. A. Sloane, Jul 15 2021

STATUS

approved