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%I #8 Dec 16 2018 17:57:52
%S 1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,3,2,1,2,1,2,1,2,1,2,1,2,1,2,
%T 1,2,1,2,3,2,1,6,1,2,1,2,1,2,1,2,1,2,1,2,1,2,3,2,1,2,1,2,3,2,5,2,1,2,
%U 1,2,1,2,1,2,1,2,1,6,1,2,1,2,1,6,1,2,1,2,1,2,1,2,3,2,1,2,1,2,1,2,1,2,1,2,3
%N a(n) = A322354(n) / A322356(n).
%H Antti Karttunen, <a href="/A322357/b322357.txt">Table of n, a(n) for n = 1..16384</a>
%H Antti Karttunen, <a href="/A322357/a322357.txt">Data supplement: n, a(n) computed for n = 1..100000</a>
%F a(n) = A322354(n) / A322356(n).
%t f[n_] := If[n == 1, 1, Times @@ Power @@@ ({#[[1]] + 2, #[[2]]} & /@ FactorInteger [n])]; rad[n_] := Times @@ (First@# & /@ FactorInteger@n); fun[p_, n_] := If[ PrimeQ[p + 2] && Divisible[n, p + 2], p + 2, 1]; a[n_] := GCD[rad[n], f[rad[n]]]/ Times @@ (fun[#, n] & /@ FactorInteger[n][[;; , 1]]); Array[a, 120] (* _Amiram Eldar_, Dec 16 2018 *)
%o (PARI)
%o A166590(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] += 2); factorback(f); };
%o A322362(n) = gcd(n, A166590(n));
%o A007947(n) = factorback(factorint(n)[, 1]);
%o A322354(n) = A322362(A007947(n));
%o A322356(n) = { my(f = factor(n), m=1); for(i=1, #f~, if(isprime(f[i,1]+2)&&!(n%(f[i,1]+2)), m *= (f[i,1]+2))); (m); };
%o A322357(n) = (A322354(n)/A322356(n));
%K nonn
%O 1,2
%A _Antti Karttunen_, Dec 16 2018
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