A231333 a(n) = lcm_{p is a prime divisor of n} (n/p - 1).

1, 0, 0, 1, 0, 2, 0, 3, 2, 4, 0, 15, 0, 6, 4, 7, 0, 40, 0, 9, 6, 10, 0, 77, 4, 12, 8, 39, 0, 630, 0, 15, 10, 16, 12, 187, 0, 18, 12, 133, 0, 260, 0, 21, 56, 22, 0, 345, 6, 72, 16, 75, 0, 442, 20, 189, 18, 28, 0, 6061, 0, 30, 40, 31, 12, 3360, 0, 33, 22, 3978

Offset

1,6

Comments

n is prime if and only if a(n) = 0.

n is a Giuga number if and only if a(n) > 0 and n divides a(n).

Links

Andrew Howroyd, Table of n, a(n) for n = 1..1000

Formula

a(6) = 2 because 6/2 - 1 = 2 and 6/3 - 1 = 1, and the least common multiple of 2 and 1 is 2.

a(7) = 0 because 7/7 - 1 = 0.

a(8) = 3 because 8/2 - 1 = 3.

Mathematica

lcm[lis_] := {aux = 1; Do[aux = LCM[aux, lis[[i]]], {i, 1, Length[lis]}]; aux}[[1]]; fa = FactorInteger; j[n_] := lcm@Table[n/fa[n][[i, 1]] - 1, {i, 1, Length[fa[n]]}] ; Array[j, 100]

Prog

(PARI) a(n)=my(f=factor(n)[, 1]); lcm(vector(#f, i, n/f[i]-1)) \\ Charles R Greathouse IV, Nov 13 2013

Crossrefs

Cf. A007850.

Sequence in context: A057860 A092915 A063749 * A357866 A331622 A212175

Adjacent sequences: A231330 A231331 A231332 * A231334 A231335 A231336

Keyword

nonn

Author

José María Grau Ribas, Nov 07 2013

Status

approved