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Integer log of 2n: sum of primes dividing 2n (with repetition).
2

%I #13 Aug 17 2019 00:59:22

%S 2,4,5,6,7,7,9,8,8,9,13,9,15,11,10,10,19,10,21,11,12,15,25,11,12,17,

%T 11,13,31,12,33,12,16,21,14,12,39,23,18,13,43,14,45,17,13,27,49,13,16,

%U 14,22,19,55,13,18,15,24,33,61,14,63,35,15,14,20,18,69,23,28,16,73,14,75

%N Integer log of 2n: sum of primes dividing 2n (with repetition).

%e a(20)=11 because 40=2^3*5^1 and 3*2+1*5=11.

%p with(numtheory): a:=proc(n) local b: b:=op(2,ifactors(n)): add(b[j][1]*b[j][2],j=1..nops(b)): end: seq(a(2*n),n=1..88); # _Emeric Deutsch_, Mar 10 2005

%t Table[Plus @@ Times @@@ FactorInteger[2n], {n, 100}] (* _Ray Chandler_, Nov 12 2005 *)

%Y Bisection of A001414.

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_, Nov 20 2004

%E More terms from _Emeric Deutsch_, Mar 10 2005