A158977 - OEIS

%I #9 Sep 08 2022 08:45:43

%S 1,2,6,24,30,720,210,6720,1890,8400,2310,47900160,30030,1681680,

%T 4054050,15375360,510510,1984862880,9699690,62078016000,1833241410,

%U 853572720,223092870,1776404640890880,5577321750,23201658480,54211567410

%N Product of the numbers k in the range 1 <= k <= n such that the proper divisors of k are a subset of the proper divisors of n.

%C Here, proper divisors include 1 but not the argument (k or n, respectively) in the divisor set, as counted in A032741.

%F If p is prime, a(p) = A034386(p).

%F a(n)*A158978(n) = A000142(n). - _R. J. Mathar_, Apr 06 2009

%e a(8) = 6720 is the product of the 7 numbers k: 1 {1}, 2 {1}, 3 {1}, 4 {1, 2}, 5 {1}, 7 {1}, 8 {1, 2, 4} with divisor set that are subsets of {1, 2, 4} for n = 8. 1 * 2 * 3 * 4 * 5 * 7 * 8 = 6720.

%o (Magma) [ &*[ k: k in [1..n] | forall(t){ d: d in Divisors(k) | d eq k or d in Divisors(n) } ]: n in [1..27] ]; // _Klaus Brockhaus_, Apr 07 2009

%Y Cf. A159073, A034386.

%K nonn

%O 1,2

%A _Jaroslav Krizek_, Apr 01 2009

%E Edited by _R. J. Mathar_, Apr 06 2009

%E More terms from _Klaus Brockhaus_, Apr 07 2009