A294874 - OEIS

%I #11 Nov 13 2017 13:22:18

%S 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,

%T 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,

%U 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

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

%H Antti Karttunen, <a href="/A294874/b294874.txt">Table of n, a(n) for n = 1..65537</a>

%H <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>

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

%F Other identities. For all n >= 1:

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

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

%e 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.

%e 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.

%o (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; };

%Y Cf. A000040, A046951, A052409, A071325.

%Y Cf. A293524, A294873, A294875.

%K nonn

%O 1,4

%A _Antti Karttunen_, Nov 11 2017