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A190846 (Squarefree part of (ABC))/C for A=1, C=A+B, as a function of B, rounded to the nearest integer. 3
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 (list; graph; refs; listen; history; text; internal format)
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 through 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

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Last modified September 25 18:51 EDT 2021. Contains 347659 sequences. (Running on oeis4.)