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A056789 Sum_{k=1..n} LCM(k,n)/GCD(k,n). 5
1, 3, 10, 19, 51, 48, 148, 147, 253, 253, 606, 352, 1015, 738, 960, 1171, 2313, 1263, 3250, 1869, 2803, 3028, 5820, 2784, 6301, 5073, 6814, 5458, 11775, 4798, 14416, 9363, 11505, 11563, 14898, 9343, 24643, 16248, 19276, 14797, 33621, 14013, 38830 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

For prime p, a(p) = 1+p*p*(p-1)/2.

a(n) > n^2*phi(n)/2. - Thomas Ordowski, Nov 08 2014

We note LCM(k,n) = k*n iff GCD(k,n) = 1 (and in general equals k*n/GCD(k,n)), and so for these values LCM/GCD = k*n. From A023896, we have that sum{k=1,..,n-1; k such that GCD(k,n)=1} is n*phi(n)/2, and so sum{k=1,..,n-1; k*n such that GCD(k,n)=1} = n * sum{k=1,..,n-1; k such that GCD(k,n)=1} = n^2*phi(n)/2. As this is true, certainly sum{k=1,..,n; LCM(k,n)/GCD(k,n)} > n^2*phi(n)/2. - Jon Perry, Nov 09 2014

LINKS

T. D. Noe, Table of n, a(n) for n=1..1000

FORMULA

a(n) = Sum_{k=1..n} k*n/gcd(k,n)^2. - Thomas Ordowski, Nov 08 2014

EXAMPLE

a(6) = 6/1 + 6/2 + 6/3 + 12/2 + 30/1 + 6/6 = 48.

MATHEMATICA

Table[ Sum[ LCM[k, n] / GCD[k, n], {k, 1, n}], {n, 1, 50}]

PROG

(Haskell)

a056789 = sum . a051537_row  -- Reinhard Zumkeller, Jul 07 2013

(PARI) vector(50, n, sum(k=1, n, lcm(k, n)/gcd(k, n))) \\ Michel Marcus, Nov 08 2014

CROSSREFS

Row sums of triangle in A051537.

Cf. A023896.

Sequence in context: A294421 A027177 A048343 * A174476 A098645 A089693

Adjacent sequences:  A056786 A056787 A056788 * A056790 A056791 A056792

KEYWORD

nonn,nice

AUTHOR

Leroy Quet, Aug 20 2000

EXTENSIONS

Additional comments from Amarnath Murthy, May 09 2002

STATUS

approved

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Last modified September 16 02:16 EDT 2019. Contains 327088 sequences. (Running on oeis4.)