A294895 a(n) = Product_{d|n, gcd(d,n/d)>1} prime(gcd(d,n/d)-1).

1, 1, 1, 2, 1, 1, 1, 4, 3, 1, 1, 4, 1, 1, 1, 20, 1, 9, 1, 4, 1, 1, 1, 16, 7, 1, 9, 4, 1, 1, 1, 100, 1, 1, 1, 396, 1, 1, 1, 16, 1, 1, 1, 4, 9, 1, 1, 400, 13, 49, 1, 4, 1, 81, 1, 16, 1, 1, 1, 16, 1, 1, 9, 1700, 1, 1, 1, 4, 1, 1, 1, 17424, 1, 1, 49, 4, 1, 1, 1, 400, 171, 1, 1, 16, 1, 1, 1, 16, 1, 81, 1, 4, 1, 1, 1, 10000, 1, 169, 9, 4508, 1, 1, 1, 16, 1

Offset: 1

Author

Antti Karttunen, Nov 21 2017

Keywords

• nonn

Comments

For all i, j: a(i) = a(j) => A294897(i) = A294897(j).

Links

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

Crossrefs

Cf. A005117 (the positions of ones).

Cf. A294876, A294897.

Programs

Mathematica

A294895[n_] := Times @@ Prime[Select[Map[GCD[#, n/#] &, Divisors[n]], #>1 &] - 1];
Array[A294895, 100] (* Paolo Xausa, Feb 22 2024 *)

PARI

A294895(n) = { my(m=1); fordiv(n,d,if(gcd(d,n/d)>1, m *= prime(gcd(d,n/d)-1))); m; };

Formula

a(n) = Product_{d|n} A008578(gcd(d,n/d)).

a(n) = A064989(A294876(n)).

For n >= 1, A001222(a(n)) = A048105(n).

For n > 1, 1+A061395(a(n)) = A000188(n).