A135323 - OEIS

%I #13 May 29 2016 13:36:44

%S 1,2,3,4,5,12,7,8,9,20,11,36,13,28,30,16,17,54,19,60,42,44,23,96,25,

%T 52,27,84,29,180,31,32,66,68,70,216,37,76,78,160,41,252,43,132,135,92,

%U 47,240,49,150,102,156,53,216,110,224,114,116,59,720,61,124,189,64,130,396

%N a(1)=1, a(n) = Sum_{p=prime, p|n} a(n/p)*p.

%C If p^k is a power of a prime, then a(p^k) = p^k.

%H Ivan Neretin, <a href="/A135323/b135323.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = n * A008480(n). - _Ivan Neretin_, May 29 2016

%e The primes that divide 12 are 2 and 3. So a(12) = a(12/2)*2 + a(12/3)*3 = 12*2 + 4*3 = 36.

%t a = {1}; For[n = 2, n < 100, n++, b = Select[Divisors[n], PrimeQ[ # ] &]; AppendTo[a, Sum[a[[n/b[[j]]]]*b[[j]], {j, 1, Length[b]}]]]; a (* _Stefan Steinerberger_, Dec 07 2007 *)

%t Fold[Append[#1, Plus @@ ((p = Select[Divisors[#2], PrimeQ])*#1[[#2/p]])] &, {1}, Range[2, 66]] (* _Ivan Neretin_, May 29 2016 *)

%K nonn

%O 1,2

%A _Leroy Quet_, Dec 06 2007

%E More terms from _Stefan Steinerberger_, Dec 07 2007