A206031 a(n) = product of numbers k <= sigma(n) such that k = sigma(d) for any divisor d of n where sigma = A000203.

1, 3, 4, 21, 6, 144, 8, 315, 52, 324, 12, 28224, 14, 576, 576, 9765, 18, 73008, 20, 95256, 1024, 1296, 24, 25401600, 186, 1764, 2080, 225792, 30, 26873856, 32, 615195, 2304, 2916, 2304, 1302170688, 38, 3600, 3136, 128595600, 42, 84934656, 44, 762048, 584064

Offset: 1

Author

Jaroslav Krizek, Feb 03 2012

Keywords

• nonn

Comments

Sequence is not the same as A206032(n): a(66) = 35831808, A206032(66) = 429981696.

In sequence A206032 are multiplied all values of sigma(d) of all divisors d of numbers n, in sequence a(n) are multiplied only distinct values of sigma(d) of all divisors d of numbers n.

Examples

			For n=6 -> divisors d of 6: 1,2,3,6; corresponding values 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 of sigma(d): 1,3,4,12,12,36,48,144; a(66) = Product of k = 1*3*4*12*36*48*144 = 35831808.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..4096

Crossrefs

Cf. A184388, A184395, A206032, A206033.

Programs

Mathematica

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

PARI

a(n)=my(d=vecsort(apply(sigma,divisors(n)),,8));prod(i=2,#d,d[i]) \\ Charles R Greathouse IV, Feb 19 2013

Formula

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