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Primorial(n) mod n!
1

%I #18 May 26 2016 14:34:28

%S 0,0,0,0,18,30,510,1470,22890,284550,3171630,18486930,45347610,

%T 4254260010,2349577230,371965003410,9252750236730,190224835871070,

%U 221717289063270,14855058367239090,1662934646118135390,45974266913148043470,4510191947325194130

%N Primorial(n) mod n!

%C a(n) mod 6 = 0 and a(n) mod 30 = 0, n<>4. - Gary Detlefs, May 02 2012

%H Harvey P. Dale, <a href="/A182254/b182254.txt">Table of n, a(n) for n = 0..449</a>

%F a(n) = A002110(n) mod A000142(n)

%e a(5) = (2*3*5*7*11) mod (1*2*3*4*5) = 2310 mod 120 = 30

%t primorial[n_] := Product[Prime[i], {i, n}]; Table[Mod[primorial[n], n!], {n, 0, 30}] (* _T. D. Noe_, Apr 21 2012 *)

%t With[{nn=30},Join[{0},Mod[#[[2]],#[[1]]]&/@Transpose[{Range[nn]!, FoldList[ Times, Prime[Range[nn]]]}]]] (* _Harvey P. Dale_, May 26 2016 *)

%Y Cf. A002110, A000142, A000040, A135568.

%K nonn

%O 0,5

%A _Alex Ratushnyak_, Apr 21 2012