A173392 - OEIS

%I #11 May 23 2018 02:44:33

%S 1,1,1,1,2,2,6,12,24,48,720,240,2160,23040,45360,40320,2419200,

%T 1935360,65318400,69672960,163296000,2786918400,754427520000,

%U 22992076800,201180672000,14714929152000,211843247616000,114776447385600,32953394073600000,2410305395097600

%N Product of nonzero remainders of n mod k, for k = 1,2,3,...,n.

%e For n = 7; 7 mod k, for k = 1,2,3,...,7: (0,1,1,3,2,1,0). Product of nonzero remainders = 6. a(7) = 6.

%t Table[Times@@DeleteCases[Mod[n, Range[n]], 0], {n, 30}]

%o (PARI) a(n) = prod(k=1, n, if (m = n % k, m, 1)); \\ _Michel Marcus_, May 23 2018

%Y Cf. A004125 (sum of remainders of n mod k).

%K nonn

%O 1,5

%A _Jaroslav Krizek_, Nov 22 2010

%E Extended by _T. D. Noe_, Nov 22 2010