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%I #15 Dec 31 2023 16:23:17
%S 0,0,0,0,0,3,0,0,3,5,0,3,0,7,8,0,0,3,0,5,10,11,0,3,5,13,3,7,0,8,0,0,
%T 14,17,12,3,0,19,16,5,0,10,0,11,8,23,0,3,7,5,20,13,0,3,16,7,22,29,0,8,
%U 0,31,10,0,18,14,0,17,26,12,0,3,0,37,8,19,18,16,0,5,3,41,0,10,22,43,32,11,0
%N Sum of odd proper distinct prime divisors of n. That is, the sum of odd distinct prime divisors of n that are less than n.
%H Robert Israel, <a href="/A091921/b091921.txt">Table of n, a(n) for n = 1..10000</a>
%F From _Robert Israel_, Jan 28 2018: (Start)
%F If n is even, a(n) = A008472(n)-2.
%F If n is prime, a(n) = A008472(n)-n = 0.
%F Otherwise, a(n) = A008472(n). (End)
%e The sum of odd proper distinct prime divisors of 15 is 8=3+5.
%p seq(convert(numtheory:-factorset(n) minus {2,n}, `+`), n=1..100); # _Robert Israel_, Jan 28 2018
%t Table[Total[Select[Most[Divisors[n]],OddQ[#]&&PrimeQ[#]&]],{n,90}] (* _Harvey P. Dale_, Dec 31 2023 *)
%o (PARI) a(n) = sumdiv(n, d, if ((d%2) && isprime(d) && (d<n), d)); \\ _Michel Marcus_, Jan 28 2018
%Y Cf. A008472, A091979, A001227.
%K easy,nonn,look
%O 1,6
%A _Mohammad K. Azarian_, Mar 16 2004
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