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A008474 If n = Product (p_j^k_j) then a(n) = Sum (p_j + k_j). 17

%I

%S 0,3,4,4,6,7,8,5,5,9,12,8,14,11,10,6,18,8,20,10,12,15,24,9,7,17,6,12,

%T 30,13,32,7,16,21,14,9,38,23,18,11,42,15,44,16,11,27,48,10,9,10,22,18,

%U 54,9,18,13,24,33,60,14,62,35,13,8,20,19,68,22,28,17,72,10,74,41,11,24,20,21

%N If n = Product (p_j^k_j) then a(n) = Sum (p_j + k_j).

%C a(1) = 0 by convention, but could equally be taken to be 1 or 2.

%C Since only the primes p_j with nonzero exponents k_j in the factorization of n are considered in Sum (p_j + k_j), to the empty product (1) should correspond the empty sum (0). a(1) = 0 is thus the most natural choice. - _Daniel Forgues_, Apr 06 2010

%C Conjecture: for m > 4, by iterating the map m -> A008474(m) one always reaches 5 [tested up to m = 320000]. - _Ivan N. Ianakiev_, Nov 10 2014

%H Reinhard Zumkeller, <a href="/A008474/b008474.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimeFactorization.html">Prime Factorization</a>

%F Additive with a(p^e) = p + e.

%p A008474 := proc(n) local e,j; e := ifactors(n)[2]:

%p add(e[j][1]+e[j][2],j=1..nops(e)) end:

%p seq (A008474(n), n=1..60);

%p # _Peter Luschny_, Jan 17 2011

%t A008474[n_]:=Plus@@Flatten[FactorInteger[n]]; Table[A008474[n], {n, 200}] (* _Zak Seidov_, May 23 2005 *)

%o (Haskell)

%o a008474 n = sum $ zipWith (+) (a027748_row n) (a124010_row n)

%o -- _Reinhard Zumkeller_, Feb 11 2012, Aug 27 2011

%o (PARI) {for(k=1, 79,

%o M=factor(k); smt =0;

%o for(i=1, matsize(M)[1], for(j=1, matsize(M)[2], smt=smt+M[i,j]));

%o print1(smt, ", "))} \\\ _Douglas Latimer_, Apr 27 2012

%o (PARI) a(n)=my(f=factor(n)); sum(i=1,#f~,f[i,1]+f[i,2]) \\ _Charles R Greathouse IV_, Jun 03 2015

%Y Cf. A107737, A107738, A000026, A027748, A124010, A250030.

%K nonn

%O 1,2

%A _Olivier GĂ©rard_

%E More terms from _Zak Seidov_, May 23 2005

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Last modified May 27 21:52 EDT 2020. Contains 334671 sequences. (Running on oeis4.)