A254939 a(n) = (A099795(n)^-1 mod p)*A099795(n), where p = prime(n).

1, 4, 36, 120, 2520, 277200, 5045040, 183783600, 4655851200, 80313433200, 32607253879200, 2743667504978400, 58772246027695200, 5038384364010597600, 56517528952814529600, 34089489546705963770400, 7391221142626702144764000

Offset: 1

Author

Bruno Berselli, Feb 12 2015 - proposed by Umberto Cerruti (Department of Mathematics "Giuseppe Peano", University of Turin, Italy)

Keywords

• nonn

Comments

The sequence lists the smallest nonnegative solutions z to the system of congruences z == 1 (mod p), z == 0 (mod v(p-1)), where p is a prime and v(p-1) = lcm(1,...,p-1).

Examples

			5045040 is the seventh term of the sequence because the modular inverse of A099795(7) mod A000040(7) is 7 and 7*A099795(7) = 7*720720 = 5045040.
		

Links

• Umberto Cerruti, Il Teorema Cinese dei Resti (in Italian), 2015. The sequence is on page 21.
• Eric Weisstein's World of Mathematics, Modular Inverse.

Crossrefs

Cf. A000040, A056604, A099795, A254924, A255010.

Programs

Magma

[Modinv(Lcm([1..p-1]),p)*Lcm([1..p-1]): p in PrimesUpTo(60)];

Maple

with(numtheory): P:=proc(q)  local a, n;  a:=[];
for n from 1 to q do a:=[op(a),n]; if isprime(n+1) then
print(lcm(op(a))*(lcm(op(a))^(-1) mod (n+1))); fi;
od; end: P(10^3); # Paolo P. Lava, Feb 16 2015

Mathematica

r[k_] := LCM @@ Range[k]; u[k_] := PowerMod[r[k - 1], -1, k] r[k - 1]; Table[u[Prime[n]], {n, 1, 20}]

PARI

a099795(n) = lcm(vector(prime(n)-1, k, k));
a(n) = {my(m = a099795(n)); m*lift(1/Mod(m, prime(n)));} \\ Michel Marcus, Feb 13 2015

Formula

a(n) = A255010(n)*A099795(n).