A225821 a(n) = Product_{p | p is prime and p, p-1 both divide n}.

1, 2, 1, 2, 1, 6, 1, 2, 1, 2, 1, 6, 1, 2, 1, 2, 1, 6, 1, 10, 1, 2, 1, 6, 1, 2, 1, 2, 1, 6, 1, 2, 1, 2, 1, 6, 1, 2, 1, 10, 1, 42, 1, 2, 1, 2, 1, 6, 1, 2, 1, 2, 1, 6, 1, 2, 1, 2, 1, 30, 1, 2, 1, 2, 1, 6, 1, 2, 1, 2, 1, 6, 1, 2, 1, 2, 1, 6, 1, 10, 1, 2, 1, 42

Offset: 1

Author

José María Grau Ribas, Jul 30 2013

Keywords

• nonn

Comments

a(n) = 2 iff n is even and is a term of A226872. - Daniel Suteu, Jul 28 2019

From Bernard Schott, Jul 30 2019: (Start)

a(n) = n if n = 1, 2, 6, 42, 1806.

a(n) = 6 if n is of the form 2^i*3^j, i and j >= 1, so if n is a term of A033845.

a(n) = 10 if n is of the form 2^i*5^j, i >= 2 and j >= 1.

a(n) = 30 if n is of the form 2^i*3^j*5^k, i >=2, j >= 1 and k >= 1. (End)

Links

• Eric M. Schmidt, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A173557, A027760.

Programs

Mathematica

fa=FactorInteger; d[m_]:= Product[If[IntegerQ[m/(fa[m][[i, 1]]-1)],fa[m][[i, 1]], 1], {i, Length@fa@m}]; Table[d[n], {n, 1, 333}]

PARI

a(n)=my(f=factor(n)[,1]); prod(i=1,#f,if(n%(f[i]-1)==0,f[i],1)) \\ Charles R Greathouse IV, Nov 13 2013

Sage

def A225821(n) : return prod(p for (p,m) in factor(n) if n%(p-1)==0) # Eric M. Schmidt, Jul 31 2013

Formula

a(n) = denominator(A031971(n)/n) = gcd(n, A027642(n)). - Daniel Suteu, Jul 28 2019