A294873 a(n) = Product_{d|n, d>1, d = x^(2k-1) for some maximal k >= 1} prime(k).

1, 2, 2, 2, 2, 8, 2, 6, 2, 8, 2, 16, 2, 8, 8, 6, 2, 16, 2, 16, 8, 8, 2, 96, 2, 8, 6, 16, 2, 128, 2, 30, 8, 8, 8, 32, 2, 8, 8, 96, 2, 128, 2, 16, 16, 8, 2, 192, 2, 16, 8, 16, 2, 96, 8, 96, 8, 8, 2, 1024, 2, 8, 16, 30, 8, 128, 2, 16, 8, 128, 2, 384, 2, 8, 16, 16, 8, 128, 2, 192, 6, 8, 2, 1024, 8, 8, 8, 96, 2, 1024, 8, 16, 8, 8, 8, 1920, 2, 16, 16, 32, 2, 128, 2

Offset: 1

Author

Antti Karttunen, Nov 11 2017

Keywords

• nonn

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, A056595, A052409, A183096.

Cf. A293524, A294874, A294875.

Programs

PARI

A294873(n) = { my(m=1,e); fordiv(n,d, if(d>1, e = ispower(d); if(!e, m += m, if((e>1)&&(e%2), m *= prime((e+1)/2))))); m; };

Formula

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

Other identities. For all n >= 1:

A001222(a(n)) = A056595(n).

A007814(a(n)) = A183096(n).