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Search: id:A008472
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| A008472 |
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a(n) = the sum of the distinct primes dividing n. |
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+0
141
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| 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, 9, 29, 10, 31, 2, 14, 19, 12, 5, 37, 21, 16, 7, 41, 12, 43, 13, 8, 25, 47, 5, 7, 7, 20, 15, 53, 5, 16, 9, 22, 31, 59, 10, 61, 33, 10, 2, 18, 16, 67, 19, 26, 14, 71, 5, 73
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Sometimes called sopf(n).
Sum of primes dividing n (without repetition) (compare A001414).
Equals A051731 * A061397 = inverse Mobius transform of [0, 2, 3, 0, 5, 0, 7,...]. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Feb 14 2008
Equals row sums of triangle A143535 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Aug 23 2008]
a(n) = n iff n is prime. [From Daniel Forgues (squid(AT)zensearch.com), Mar 24 2009]
a(n) = n is a new record iff n is prime. [From Zak Seidov (zakseidov(AT)yahoo.com), Jun 27 2009]
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LINKS
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Daniel Forgues, Table of n, a(n) for n=1..100000
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FORMULA
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n = Product(p_j^k_j) -> Sum (p_j).
Additive with a(p^e) = p.
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]
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MAPLE
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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;
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]
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MATHEMATICA
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Prepend[ Array[ Plus @@ First[ Transpose[ FactorInteger[ # ] ] ]&, 100, 2 ], 0 ]
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PROGRAM
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(PARI) sopf(n) = local(fac, i); fac=factor(n); sum(i=1, matsize(fac)[1], fac[i, 1])
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CROSSREFS
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Cf. A001414 (sopfr), A001222.
Cf. A051731, A061397.
A143535 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Aug 23 2008]
Cf. A085020 [From Peter Luschny (peter(AT)luschny.de), May 04 2009]
Sequence in context: A095402 A086294 A075860 this_sequence A123528 A074036 A074251
Adjacent sequences: A008469 A008470 A008471 this_sequence A008473 A008474 A008475
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KEYWORD
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nonn,nice
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AUTHOR
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Olivier Gerard (olivier.gerard(AT)gmail.com)
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