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A116477
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a(n) = sum{1<=k<=n, GCD(k,n)=1} floor(n/k).
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3
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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; internal format)
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OFFSET
| 1,2
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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). [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Aug 07 2008]
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FORMULA
| a(n) also is sum{k|n} mu(n/k) (sum{j=1 to k} d(j)) and is sum{1<=k<=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.
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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.
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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);
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MATHEMATICA
| Table[a := Select[Range[n], GCD[n, # ] == 1 &]; Sum[Floor[n/a[[i]]], {i, 1, Length[a]}], {n, 1, 60}]
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PROG
| (PARI) A116477(n) = sum(k=1, n, (gcd(k, n)==1)*floor(n/k)) [From Michael B. Porter (michael_b_porter(AT)yahoo.com), Mar 01 2010]
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CROSSREFS
| Cf. A006218. Row sums of A122191.
A054525 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Aug 07 2008]
Sequence in context: A011175 A109534 A011341 * A116920 A116919 A167511
Adjacent sequences: A116474 A116475 A116476 * A116478 A116479 A116480
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KEYWORD
| easy,nonn
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AUTHOR
| Leroy Quet Mar 18 2006
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EXTENSIONS
| More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu) and Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Apr 01 2006
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