A190846 (Squarefree part of (ABC))/C for A=1, C=A+B, as a function of B, rounded to the nearest integer.

1, 2, 2, 2, 5, 6, 2, 1, 3, 10, 6, 6, 13, 14, 2, 2, 6, 6, 10, 10, 21, 22, 6, 1, 5, 3, 2, 14, 29, 30, 2, 2, 33, 34, 6, 6, 37, 38, 10, 10, 41, 42, 22, 7, 15, 46, 6, 1, 1, 10, 26, 26, 6, 6, 14, 14, 57, 58, 30, 30, 61, 21, 1, 2, 65, 66, 34, 34, 69, 70, 6, 6, 73, 15, 8, 38, 77, 78, 10, 0, 3, 82, 42

Offset

1,2

Comments

Given A, B natural numbers, and C=A+B, the ABC conjecture deals with the ratio of the squarefree part of the product A*B*C, divided by C. Here, B plays the role of the OEIS index n.

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Abderrahmane Nitaj, The ABC conjecture homepage

Eric Weisstein's World of Mathematics, abc Conjecture

Wikipedia, ABC conjecture

Example

For B=14, we have C=15, so SQP(ABC)=SQP(210)=2*3*5*7=210, so SQP(ABC)/C=210/15=14.
For B=19, we have C=20, so SQP(ABC)=SQP(380)=2*5*19=190, so SQP(ABC)/C=190/20=9.5, which rounds to 10.

Maple

A190846 := proc(n) c := 1+n ; round(A007947(n*c)/c) ; end proc:
seq(A190846(n), n=1..80) ; # R. J. Mathar, Jun 10 2011

Mathematica

Array[Round[SelectFirst[Reverse@ Divisors[#1 #2], SquareFreeQ]/#2] & @@ {#, # + 1} &, 83] (* Michael De Vlieger, Feb 19 2019 *)

Prog

(Magma) SQP:=func< n | &*[ f[j, 1]: j in [1..#f] ] where f is Factorization(n) >; A190846:=func< n | Round(SQP(a*n*c)/c) where c is a+n where a is 1 >; [ A190846(n): n in [1..85] ]; // Klaus Brockhaus, May 27 2011
(PARI) rad(n)=my(f=factor(n)[, 1]); prod(i=1, #f, f[i])
a(n)=rad(n^2+n)\/(n+1) \\ Charles R Greathouse IV, Mar 11 2014
(Python)
from operator import mul
from sympy import primefactors
def rad(n): return 1 if n<2 else reduce(mul, primefactors(n))
def a(n): return int(round(rad(n**2 + n)/(n + 1))) # Indranil Ghosh, May 24 2017

Crossrefs

Cf. A191093, A191100, A120498.

Sequence in context: A326686 A096403 A073819 * A214787 A066835 A123953

Adjacent sequences: A190843 A190844 A190845 * A190847 A190848 A190849

Keyword

nonn,easy

Author

Darrell Minor, May 25 2011

Status

approved