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A116477 a(n) = Sum_{1<=k<=n, gcd(k,n)=1} floor(n/k). 5
1, 2, 4, 5, 9, 7, 15, 12, 18, 15, 28, 16, 36, 23, 31, 30, 51, 26, 59, 34, 50, 43, 75, 37, 77, 52, 72, 55, 102, 42, 112, 69, 90, 73, 106, 61, 141, 84, 109, 80, 159, 66, 169, 97, 119, 108, 187, 84, 185, 103, 155, 121, 218, 97, 193, 126, 179, 142, 248, 95, 262, 152, 185 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

sum{k|n} a(k) = sum{k=1 to n} d(k), where d(k) is the number of positive divisors of k.

Equals A054525 * A006218 (Mobius transform of A006218). - Gary W. Adamson, Aug 07 2008

LINKS

Table of n, a(n) for n=1..63.

FORMULA

a(n) is also Sum_{k|n} mu(n/k) (Sum_{j=1..k} d(j)) and Sum_{k=1..n} phi(n,n/k), where mu() is the Mobius (Moebius) function, d(j) is the number of positive divisors of j and phi(n,x) is the number of positive integers which are <= x and are coprime to n.

EXAMPLE

a(6)=7 because the numbers relatively prime to 6 and not exceeding 6 are 1 and 5, yielding floor(6/1) + floor(6/5) = 7.

MAPLE

a:=proc(n) local s, j: s:=0: for j from 1 to n do if gcd(j, n)=1 then s:=s+floor(n/j) else s:=s: fi od: s: end: seq(a(n), n=1..75);

MATHEMATICA

Table[a := Select[Range[n], GCD[n, # ] == 1 &]; Sum[Floor[n/a[[i]]], {i, 1, Length[a]}], {n, 1, 60}]

PROG

(PARI) A116477(n) = sum(k=1, n, (gcd(k, n)==1)*floor(n/k)) \\ Michael B. Porter, Mar 01 2010

CROSSREFS

Cf. A006218. Row sums of A122191.

Cf. A054525. - Gary W. Adamson, Aug 07 2008

Sequence in context: A109534 A276163 A011341 * A116920 A116919 A270429

Adjacent sequences:  A116474 A116475 A116476 * A116478 A116479 A116480

KEYWORD

easy,nonn

AUTHOR

Leroy Quet, Mar 18 2006

EXTENSIONS

More terms from Emeric Deutsch and Stefan Steinerberger, Apr 01 2006

STATUS

approved

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Last modified April 10 02:39 EDT 2020. Contains 333392 sequences. (Running on oeis4.)