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A083344 a(n)=A082457(n)-A066715(n)= GCD[2n+1, A057643(2n+1)]-GCD[2n+1, A000203(2n+1)]. 4
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 0, 0, 30, 0, 0, 0, 0, 0, 0, 4, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,22

LINKS

Table of n, a(n) for n=1..124.

FORMULA

a(n)=GCD[2n+1, LCM[1+D(2n+1)]]-GCD[2n+1, sigma(2n+1)], GCD[2n+1, A057643(2n+1)]-GCD[2n+1, A000203(2n+1)], where D(x)=divisor-set of x

EXAMPLE

n=22: 2n+1=45, A057643(45)=5520, a(22)=GCD[45,5520]=15 while A066715[45]=3; a(22)=15-3=12; sites where nonzero terms appear see in A082452.

MATHEMATICA

di[x_] := Apply[LCM, Divisors[x]+1] (*A066715=*)t1=Table[GCD[2*n+1, DivisorSigma[1, 2*n+1]], {n, 1, 2048}]; (*A082457=*)t2=Table[GCD[2*w+1, di[1+2*w]], {w, 1, 2048}]; (*A083344=*)t2-t1;

PROG

(PARI) a(n)=gcd(lcm(apply(d->d+1, divisors(2*n+1))), 2*n+1)-gcd(sigma(2*n+1), 2*n+1) \\ Charles R Greathouse IV, Feb 14 2013

CROSSREFS

Cf. A057643, A066715, A000203, A082457, A082452.

Sequence in context: A243534 A257304 A241570 * A063863 A236238 A187795

Adjacent sequences:  A083341 A083342 A083343 * A083345 A083346 A083347

KEYWORD

sign

AUTHOR

Labos Elemer, Apr 25 2003

STATUS

approved

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Last modified March 30 16:23 EDT 2017. Contains 284302 sequences.