This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A254939 a(n) = (A099795(n)^-1 mod p)*A099795(n), where p = prime(n). 3
 1, 4, 36, 120, 2520, 277200, 5045040, 183783600, 4655851200, 80313433200, 32607253879200, 2743667504978400, 58772246027695200, 5038384364010597600, 56517528952814529600, 34089489546705963770400, 7391221142626702144764000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 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). 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. FORMULA a(n) = A255010(n)*A099795(n). EXAMPLE 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. 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}] PROG (MAGMA) [Modinv(Lcm([1..p-1]), p)*Lcm([1..p-1]): p in PrimesUpTo(60)]; (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 CROSSREFS Cf. A000040, A056604, A099795, A254924, A255010. Sequence in context: A016826 A190318 A193874 * A038688 A076830 A144298 Adjacent sequences:  A254936 A254937 A254938 * A254940 A254941 A254942 KEYWORD nonn AUTHOR Bruno Berselli, Feb 12 2015 - proposed by Umberto Cerruti (Department of Mathematics "Giuseppe Peano", University of Turin, Italy) STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 7 09:33 EST 2019. Contains 329843 sequences. (Running on oeis4.)