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A069359
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a(1)=0; for n>1, a(n)=n*sum(p|n,1/p) where p are primes dividing n.
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3
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0, 1, 1, 2, 1, 5, 1, 4, 3, 7, 1, 10, 1, 9, 8, 8, 1, 15, 1, 14, 10, 13, 1, 20, 5, 15, 9, 18, 1, 31, 1, 16, 14, 19, 12, 30, 1, 21, 16, 28, 1, 41, 1, 26, 24, 25, 1, 40, 7, 35, 20, 30, 1, 45, 16, 36, 22, 31, 1, 62, 1, 33, 30, 32, 18, 61, 1, 38, 26, 59, 1, 60, 1, 39, 40, 42, 18, 71, 1, 56
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| Also arithmetic derivative of squarefree numbers: a(A005117(n)) = A068328(n) = A003415(A005117(n)). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jul 20 2003
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FORMULA
| G.f.: Sum(x^p(j)/(1-x^p(j))^2,j=1..infinity), where p(j) is the j-th prime. - Vladeta Jovovic (vladeta(AT)eunet.rs), Mar 29 2006
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MAPLE
| A069359 := n -> add(n/d, d = select(isprime, numtheory[divisors](n))):
seq(A069359(i), i = 1..20); # Peter Luschny, Jan 31 2012
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PROG
| (Sage)
def A069359(n) :
D = filter(is_prime, divisors(n))
return add(n/d for d in D)
print [A069359(i) for i in (1..20)] # Peter Luschny, Jan 31 2012
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CROSSREFS
| Sequence in context: A161686 A069626 A205443 * A014652 A060448 A090080
Adjacent sequences: A069356 A069357 A069358 * A069360 A069361 A069362
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KEYWORD
| easy,nonn
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AUTHOR
| Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 15 2002
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