1,2

Sequence is not the same as A206031(n): a(66) = 429981696, A206031(66) = 35831808.

In sequence a(n) are multiplied all values of sigma(d) of all divisors d of numbers n, in sequence A206031 are multiplied only distinct values of sigma(d) of all divisors d of numbers n.

G. C. Greubel, Table of n, a(n) for n = 1..1000

a(p) = p+1, a(pq) = ((p+1)*(q+1))^2 for p, q = distinct primes.

For n=6 -> divisors d of 6: 1,2,3,6; corresponding values k of sigma(d): 1,3,4,12; a(6) = Product of k = 1*3*4*12 = 144. For n=66 -> divisors d of 66: 1,2,3,6,11,22,33,66; corresponding values k of sigma(d): 1,3,4,12,12,36,48,144; a(66) = Product of k = 1*3*4*12*12*36*48*144 = 429981696.

Table[Times @@ DivisorSigma[1, Divisors[n]], {n, 100}] (* T. D. Noe, Feb 10 2012 *)

(PARI) a(n)=my(d=divisors(n)); prod(i=2, #d, sigma(d[i])) \\ Charles R Greathouse IV, Feb 19 2013

Cf. A184388, A206031, A206033.

Sequence in context: A324985 A069934 A206031 * A197410 A308689 A339482

Adjacent sequences: A206029 A206030 A206031 * A206033 A206034 A206035

Jaroslav Krizek, Feb 03 2012

approved