%I A008472
%S A008472 0,2,3,2,5,5,7,2,3,7,11,5,13,9,8,2,17,5,19,7,10,13,23,5,5,15,3,
%T A008472 9,29,10,31,2,14,19,12,5,37,21,16,7,41,12,43,13,8,25,47,5,7,7,20,
%U A008472 15,53,5,16,9,22,31,59,10,61,33,10,2,18,16,67,19,26,14,71,5,73
%N A008472 a(n) = the sum of the distinct primes dividing n.
%C A008472 Sometimes called sopf(n).
%C A008472 Sum of primes dividing n (without repetition) (compare A001414).
%C A008472 Equals A051731 * A061397 = inverse Mobius transform of [0, 2, 3, 0, 5, 
               0, 7,...]. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Feb 14 2008
%C A008472 Equals row sums of triangle A143535 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), 
               Aug 23 2008]
%C A008472 a(n) = n iff n is prime. [From Daniel Forgues (squid(AT)zensearch.com), 
               Mar 24 2009]
%C A008472 a(n) = n is a new record iff n is prime. [From Zak Seidov (zakseidov(AT)yahoo.com), 
               Jun 27 2009]
%H A008472 Daniel Forgues, <a href="b008472.txt">Table of n, a(n) for n=1..100000</
               a>
%F A008472 n = Product(p_j^k_j) -> Sum (p_j).
%F A008472 Additive with a(p^e) = p.
%F A008472 G.f. sum(k>=1, prime(k)*x^prime(k)/(1-x^prime(k))). [From Franklin T. 
               Adams-Watters (FrankTAW(AT)Netscape.net), Sep 01 2009]
%p A008472 A008472 := proc(n) local t1,i; if n=1 then RETURN(0) else t1 := 0; for 
               i from 1 to n do if n mod ithprime(i) = 0 then t1 := t1+ithprime(i); 
               fi; od; fi; t1; end;
%p A008472 T := proc(n,k) local i; numtheory[divisors](n); select(isprime, map(i->
               i+k, %)); add(i,i=%) end: seq(T(n,0),n=1..20); [From Peter Luschny 
               (peter(AT)luschny.de), May 04 2009]
%t A008472 Prepend[ Array[ Plus @@ First[ Transpose[ FactorInteger[ # ] ] ]&, 100, 
               2 ], 0 ]
%o A008472 (PARI) sopf(n) = local(fac, i); fac=factor(n); sum(i=1,matsize(fac)[1],
               fac[i,1])
%Y A008472 Cf. A001414 (sopfr), A001222.
%Y A008472 Cf. A051731, A061397.
%Y A008472 A143535 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Aug 23 2008]
%Y A008472 Cf. A085020 [From Peter Luschny (peter(AT)luschny.de), May 04 2009]
%Y A008472 Sequence in context: A095402 A086294 A075860 this_sequence A123528 A074036 
               A074251
%Y A008472 Adjacent sequences: A008469 A008470 A008471 this_sequence A008473 A008474 
               A008475
%K A008472 nonn,nice
%O A008472 1,2
%A A008472 Olivier Gerard (olivier.gerard(AT)gmail.com)