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A109352
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a(n) = sum of the prime divisors of the n-th squarefree composite number.
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1
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5, 7, 9, 8, 10, 13, 15, 10, 14, 19, 12, 21, 16, 12, 25, 20, 16, 22, 31, 33, 18, 16, 26, 14, 39, 18, 18, 43, 22, 45, 32, 20, 34, 49, 24, 22, 15, 55, 18, 40, 24, 28, 61, 24, 63, 44, 46, 20, 26, 69, 28, 50, 73, 24, 34, 75, 20, 36, 81, 56, 30, 19, 85, 24, 34, 62, 91, 22, 64, 42, 36
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OFFSET
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1,1
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COMMENTS
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Similar to the definition of A120944 except we list the sum of the divisors of n instead of n.
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LINKS
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FORMULA
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EXAMPLE
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The 3rd squarefree composite number is 14 = 2*7, so a(3) = 2 + 7 = 9.
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MAPLE
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map(t-> convert(numtheory:-factorset(t), `+`), select(numtheory:-issqrfree and not isprime, [$6..1000])); # Robert Israel, Oct 09 2015
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MATHEMATICA
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lim = 200; Total@ Map[First, FactorInteger@ #] & /@ Select[Range@ lim, SquareFreeQ@ # && CompositeQ@ # &] (* Michael De Vlieger, Oct 09 2015 *)
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PROG
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(PARI) distinct(n) = \\ Sum of the distinct divisors p1, p2.. of n
if p1*p2..=n { local(a, x, m, p, ln, s); for(m=2, n, p=1; s=0; a=ifactord(m); ln=length(a); if(ln > 1, for(x=1, ln, p*=a[x]; s+=a[x]; ) ); if(p==m, print1(s", ") ) ) }
ifactord(n, m=0) = \\The vector of the distinct integer factors of n.
{ local(f, j, k, flist); flist=[]; f=Vec(factor(n, m)); for(j=1, length(f[1]), flist = concat(flist, f[1][j]) ); return(flist) }
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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