A294874 a(n) = Product_{d|n, d>1, d = x^(2k) for some maximal k} prime(k).

1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 6, 1, 2, 1, 2, 1, 1, 1, 2, 2, 1, 2, 2, 1, 1, 1, 6, 1, 1, 1, 8, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 6, 2, 2, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 2, 30, 1, 1, 1, 2, 1, 1, 1, 8, 1, 1, 2, 2, 1, 1, 1, 6, 6, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 6, 1, 2, 2, 8, 1, 1, 1, 2, 1, 1, 1, 8, 1, 1, 1, 6, 1, 1, 1, 2, 2, 1, 1, 2

Offset: 1

Author

Antti Karttunen, Nov 11 2017

Keywords

• nonn

Examples

			For n = 36, it has three square-divisors: 4 = 2^(2*1), 9 = 3^(2*1) and 36 = 6^(2*1). Thus a(36) = prime(1) * prime(1) * prime(1) = 2*2*2 = 8.
For n = 64, it has three square-divisors: 4 = 2^(2*1), 16 = 2^(2*2) and 64 = 2^(2*3). Thus a(64) = prime(1) * prime(2) * prime(3) = 2*3*5 = 30.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences computed from exponents in factorization of n

Crossrefs

Cf. A000040, A046951, A052409, A071325.

Cf. A293524, A294873, A294875.

Programs

PARI

A294874(n) = { my(m=1,e); fordiv(n,d, if(d>1, e = ispower(d); if((e>1)&&!(e%2), m *= prime(e/2)))); m; };

Formula

a(n) = Product_{d|n, d>1, r = A052409(d) is even} A000040(r/2).

Other identities. For all n >= 1:

A001222(a(n)) = A071325(n).

1 + A001222(a(n)) = A046951(n).