A173956 n-th primorial modulo n.

0, 0, 0, 2, 0, 0, 0, 2, 6, 0, 0, 6, 0, 0, 0, 10, 0, 12, 0, 10, 0, 0, 0, 6, 20, 0, 3, 14, 0, 0, 0, 22, 0, 0, 0, 6, 0, 0, 0, 30, 0, 0, 0, 22, 30, 0, 0, 18, 21, 40, 0, 26, 0, 30, 0, 42, 0, 0, 0, 30, 0, 0, 42, 18, 0, 0, 0, 34, 0, 0, 0, 30, 0, 0, 60, 38, 0, 0, 0, 50, 12, 0, 0, 42, 0, 0, 0, 66, 0, 30, 0

Offset: 1

Author

Carl R. White, Mar 03 2010

Keywords

• easy
• nonn

Comments

Very similar to A076998.

For all n, a(A013929(n)) != 0, and a(A005117(n)) = 0. - Michel Marcus, Sep 03 2013 and Antti Karttunen, Nov 20 2017

Examples

			a(9) = p(9)# mod 9 = 23# mod 9 = 2*3*5*7*11*13*17*19*23 mod 9 = 6.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384

Crossrefs

Cf. A002110, A005117 (the positions of zeros).

Differs from A076998 for the first time at n=16, where a(16) = 10, while A076998(16) = 2.

Programs

Mathematica

Array[Mod[Product[Prime@ i, {i, #}], #] &, 91] (* Michael De Vlieger, Nov 20 2017 *)
Module[{nn=100,prlm},prlm=FoldList[Times,Prime[Range[nn]]];Mod[ #[[1]], #[[2]]]&/@ Thread[{prlm,Range[nn]}]] (* Harvey P. Dale, May 14 2022 *)

PARI

a(n) =  prod(i=1, n, prime(i)) % n; \\ Michel Marcus, Sep 03 2013

Formula

a(n) = A002110(n) mod n. - Michel Marcus, Sep 03 2013