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A179017 Odd numbers c such that c(c^2-1)/4 is squarefree. 4
3, 5, 11, 13, 21, 29, 43, 59, 61, 67, 69, 77, 83, 85, 93, 115, 123, 131, 133, 139, 141, 155, 157, 165, 173, 187, 203, 205, 211, 213, 219, 221, 227, 229, 237, 259, 267, 277, 283, 285, 291, 309, 317, 331, 347, 355, 357, 365, 371, 373, 381, 389, 403, 411, 419, 421 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Original title was: "Numbers c such that (c^2-1)c is square free and gcd(c-1,c,c+1)=1", but (c^2-1)c is never squarefree for odd c, and gcd(n,n+1) is always = 1. - M. F. Hasler, Nov 03 2013

These numbers c with distribution a+b=c such that a=(c-1)/2 (see A172186) and b=(c+1)/2 (see A179019) have minimal possible values with function L(a,b,c)=log(c)/log(N(a,b,c)) = log(c)/log((c^2-1)c/4).

This function is minimal orbital in hypothesis (a,b,c).

There are no numbers or distributions which have value L less than log(c)/log((c^2-1)c/4).

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

MATHEMATICA

aa = {}; Do[If[(GCD[x, (x - 1)/2] == 1) && (GCD[x, (x + 1)/2] == 1) && (GCD[(x - 1)/2, (x + 1)/2] == 1), If[SquareFreeQ[(x^2 - 1) x/4], AppendTo[aa, x]]], {x, 2, 1000}]; aa

PROG

(PARI) forstep(n=3, 421, 2, issquarefree(n*(n^2-1)/4)&&print1(n", ")) \\ - M. F. Hasler, Nov 03 2013

(PARI) is(n)=n%2 && issquarefree(n) && issquarefree(n^2\4) \\ Charles R Greathouse IV, Mar 11 2014

CROSSREFS

Cf. A172120, A172121, A147298, A147299, A147300, A147301, A147302, A147306, A147307, A147638, A147639, A147640, A147641, A147642, A147643, A143700, A172186, A179019.

Sequence in context: A156221 A207325 A295243 * A078971 A266723 A129096

Adjacent sequences:  A179014 A179015 A179016 * A179018 A179019 A179020

KEYWORD

nonn

AUTHOR

Artur Jasinski, Jun 24 2010

EXTENSIONS

Edited by M. F. Hasler, Nov 03 2013

STATUS

approved

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Last modified May 16 03:58 EDT 2022. Contains 353688 sequences. (Running on oeis4.)