A260624 a(n) = arithmetic derivative of the n-th composite number.

4, 5, 12, 6, 7, 16, 9, 8, 32, 21, 24, 10, 13, 44, 10, 15, 27, 32, 31, 80, 14, 19, 12, 60, 21, 16, 68, 41, 48, 39, 25, 112, 14, 45, 20, 56, 81, 16, 92, 22, 31, 92, 33, 51, 192, 18, 61, 72, 26, 59, 156, 39, 55, 80, 18, 71, 176, 108, 43, 124, 22, 45, 32, 140, 123

Offset: 1

Author

Matthew Campbell, Oct 06 2015

Keywords

• nonn
• easy

Examples

			The second composite number is 6. 6 = 2 * 3. 6' = 2*3' + 3*2' = 3 * 1 + 2 * 1 = 3 + 2 = 5, so a(2) = 5.
		

Links

• Matthew Campbell, Table of n, a(n) for n = 1..10000; used code by _Altug Alkan_.

Crossrefs

Cf. A002808 (composite), A003415 (n').

Cf. A001787 ((2^n)'), A068719 ((2*n)'), A068720 ((n^2)'), A068721 ((n^3)').

Programs

Mathematica

lim = 120; f[n_] := If[Abs@ n < 2, 0, n Total[#2/#1 & @@@ FactorInteger[Abs@ n]]]; f /@ Rest@ Complement[Range@ lim, Prime@ Range@ PrimePi@ lim] (* Michael De Vlieger, Oct 07 2015, after Michael Somos at A003415 *)

PARI

forcomposite(n=1, 100, if((a(n) = local(fac); if(n<1, 0, fac=factor(n); sum(i=1, matsize(fac)[1], n*fac[i, 2]/fac[i, 1]))), print1(a(n)", "))); \\ Altug Alkan, Oct 06 2015

Formula

a(n) = A003415(A002808(n)).

Extensions

More terms from Altug Alkan, Oct 06 2015