A029933 - OEIS

%I #23 Sep 28 2019 03:25:46

%S 2,6,8,15,12,28,16,135,80,198,24,455,28,360,256,2295,36,2660,40,2079,

%T 1408,828,48,11375,312,1134,2240,6525,60,76384,64,75735,1088,1890,

%U 3456,1599325,76,2340,4480,767151,84

%N Numerator of n * Product_{d|n} (1 + 1/d).

%H Amiram Eldar, <a href="/A029933/b029933.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Harvey P. Dale)

%F Given p prime, a(p) = 2p + 2, since p(1 + 1/1)(1 + 1/p) = 2p + 2, see A089241. - _Alonso del Arte_, Mar 02 2017

%e a(6) = 28. The divisors of 6 are 1, 2, 3, 6. We multiply 2 * (1 + 1/2)(1 + 1/3)(1 + 1/6) to get 14/3, which multiplied by 6 is 28.

%e a(7) = 16, since 2 * 7 + 2 = 16.

%e a(8) = 135. The divisors of 8 are 1, 2, 4, 8. We multiply 2 * (1 + 1/2)(1 + 1/4)(1 + 1/8) to get 135/32, which multiplied by 8 is 135/4, the numerator of which is 135.

%p with(numtheory): A029933 := proc(n) local i,j; j := n; for i in divisors(n) do j := j*(1+1/i); od; end;

%t Numerator[Table[n * Times@@((1 + 1/#)&/@Divisors[n]), {n, 50}]] (* _Harvey P. Dale_, Dec 14 2014 *)

%o (PARI) a(n) = my(d=divisors(n)); numerator(n*prod(i=1, #d, (d[i]+1)/d[i])); \\ _Michel Marcus_, Mar 06 2017

%Y Cf. A029934 (denominators).

%K nonn,frac

%O 1,1

%A _N. J. A. Sloane_