A294875 - OEIS

%I #15 Nov 13 2017 13:22:28

%S 1,1,1,2,1,1,1,6,2,1,1,2,1,1,1,30,1,2,1,2,1,1,1,6,2,1,6,2,1,1,1,210,1,

%T 1,1,8,1,1,1,6,1,1,1,2,2,1,1,30,2,2,1,2,1,6,1,6,1,1,1,2,1,1,2,2310,1,

%U 1,1,2,1,1,1,24,1,1,2,2,1,1,1,30,30,1,1,2,1,1,1,6,1,2,1,2,1,1,1,210,1,2,2,8,1,1,1,6,1,1,1,24,1,1,1,30,1,1,1,2

%N a(n) = Product_{d|n, d = x^k, with x,k > 1} prime(A052409(d)-1).

%C For all i, j:

%C   a(i) = a(j) => A294874(i) = A294874(j) => A046951(i) = A046951(j).

%C   a(i) = a(j) => A061704(i) = A061704(j).

%H Antti Karttunen, <a href="/A294875/b294875.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} A008578(A052409(d)).

%F a(n) = A064989(A293524(n)).

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

%F 1 + A001222(a(n)) = A091050(n).

%o (PARI) A294875(n) = { my(m=1,e); fordiv(n,d, if(d>1, e = ispower(d); if(e>1, m *= prime(e-1)))); m; };

%Y Cf. A000040, A001597, A052409.

%Y Cf. A293524, A294873, A294874.

%Y Cf. A046951, A061704, A091050 (some of the matched sequences).

%K nonn

%O 1,4

%A _Antti Karttunen_, Nov 11 2017