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a(n) = Product_{d|n, d>1} A008578(1+A286561(sigma(n),d)), where A286561(n,d) gives the highest exponent of d dividing n.
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%I #9 Sep 18 2019 16:14:08

%S 1,1,1,1,1,12,1,1,1,2,1,6,1,5,2,1,1,2,1,2,1,3,1,48,1,2,1,80,1,45,1,1,

%T 2,2,1,1,1,3,1,8,1,44,1,6,2,5,1,6,1,1,3,2,1,20,1,20,1,2,1,80,1,11,1,1,

%U 1,63,1,2,2,7,1,2,1,2,1,6,1,20,1,2,1,2,1,264,1,3,2,6,1,48,2,10,1,7,2,108,1,1,2,1,1,125,1,2,2

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

%H Antti Karttunen, <a href="/A327154/b327154.txt">Table of n, a(n) for n = 1..16384</a>

%H Antti Karttunen, <a href="/A327154/a327154.txt">Data supplement: n, a(n) computed for n = 1..65537</a>

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

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

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

%o (PARI) A327154(n) = { my(m=1,s=sigma(n),v); fordiv(n,d,if((d>1) && ((v = valuation(s,d))>0), m *= prime(v))); (m); };

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

%Y Cf. also A293514, A322312, A323155, A327155, A327156.

%K nonn

%O 1,6

%A _Antti Karttunen_, Sep 18 2019