login
a(n) = Product_{d|sigma(n), d>1} A008578(1+A286561(n,d)), where A286561(n,d) gives the highest exponent of d dividing n.
4

%I #6 Sep 18 2019 16:14:16

%S 1,1,1,1,1,8,1,1,1,2,1,6,1,2,2,1,1,3,1,3,1,2,1,80,1,2,1,48,1,8,1,1,2,

%T 2,1,1,1,2,1,20,1,8,1,6,3,2,1,21,1,1,2,3,1,20,1,20,1,2,1,48,1,2,1,1,1,

%U 8,1,3,2,2,1,3,1,2,1,6,1,8,1,7,1,2,1,48,1,2,2,10,1,48,2,6,1,2,2,264,1,1,3,1,1,8,1,5,2

%N a(n) = Product_{d|sigma(n), d>1} A008578(1+A286561(n,d)), where A286561(n,d) gives the highest exponent of d dividing n.

%H Antti Karttunen, <a href="/A327155/b327155.txt">Table of n, a(n) for n = 1..16384</a>

%H Antti Karttunen, <a href="/A327155/a327155.txt">Data supplement: n, a(n) computed for n = 1..65537</a>

%F a(n) = Product_{d|sigma(n), d>1} A008578(1+A286561(n,d)), where sigma = A000203.

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

%F 1+A001222(a(n)) = A073802(n).

%o (PARI) A327155(n) = { my(m=1,v); fordiv(sigma(n),d,if((d>1) && ((v = valuation(n,d))>0), m *= prime(v))); (m); };

%Y Cf. A000040, A008578, A286561, A073802.

%Y Cf. also A293514, A322312, A323155, A327154, A327156.

%K nonn

%O 1,6

%A _Antti Karttunen_, Sep 18 2019