OFFSET
1,1
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)
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
EXAMPLE
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.
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 *)
PROG
(PARI) a(n) = my(d=divisors(n)); numerator(n*prod(i=1, #d, (d[i]+1)/d[i])); \\ Michel Marcus, Mar 06 2017
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
STATUS
approved