A206033 a(1) =1; for n>=1: a(n) = product of numbers k <= sigma(n) such that k is not equal to sigma(d) for any divisor d of n where sigma = A000203.

1, 2, 6, 240, 120, 3326400, 5040, 4151347200, 119750400, 19760412672000, 39916800, 10802449851605508096000000, 6227020800, 1077167364120207360000, 1077167364120207360000, 842072570832352567099392000000, 355687428096000

Offset: 1

Author

Jaroslav Krizek, Feb 03 2012

Keywords

• nonn

Comments

In sequence A206032 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 and in sequence a(n) are multiplied numbers k (1<=k<=sigma(n)) such that sigma(d) = k has no solution for neither divisor d of number 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 = 2*5*6*7*8*9*10*11 = 3326400.
		

Crossrefs

Cf. A184388, A206031, A206032.

Programs

Mathematica

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