

A109352


a(n) = sum of the prime divisors of the nth squarefree composite number.


1



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

1,1


COMMENTS

Similar to the definition of A120944 except we list the sum of the divisors of n instead of n.


LINKS

Robert Israel, Table of n, a(n) for n = 1..10000


FORMULA

a(n) = A008472(A120944(n)) = A001414(A120944(n)).


EXAMPLE

The 3rd squarefree composite number is 14 = 2*7, so a(3) = 2 + 7 = 9.


MAPLE

map(t> convert(numtheory:factorset(t), `+`), select(numtheory:issqrfree and not isprime, [$6..1000])); # Robert Israel, Oct 09 2015


MATHEMATICA

lim = 200; Total@ Map[First, FactorInteger@ #] & /@ Select[Range@ lim, SquareFreeQ@ # && CompositeQ@ # &] (* Michael De Vlieger, Oct 09 2015 *)


PROG

(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) }


CROSSREFS

Cf. A000469, A001414, A008472, A120944.
Sequence in context: A177705 A135913 A308713 * A228578 A242742 A323602
Adjacent sequences: A109349 A109350 A109351 * A109353 A109354 A109355


KEYWORD

easy,nonn


AUTHOR

Cino Hilliard, Aug 21 2005


STATUS

approved



