A029933 Numerator of n * Product_{d|n} (1 + 1/d).

2, 6, 8, 15, 12, 28, 16, 135, 80, 198, 24, 455, 28, 360, 256, 2295, 36, 2660, 40, 2079, 1408, 828, 48, 11375, 312, 1134, 2240, 6525, 60, 76384, 64, 75735, 1088, 1890, 3456, 1599325, 76, 2340, 4480, 767151, 84

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• frac

Examples

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

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)

Crossrefs

Cf. A029934 (denominators).

Programs

Maple

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

Mathematica

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

PARI

a(n) = my(d=divisors(n)); numerator(n*prod(i=1, #d, (d[i]+1)/d[i])); \\ Michel Marcus, Mar 06 2017

Formula

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