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A348037 a(n) = n / gcd(n, A003968(n)), where A003968 is multiplicative with a(p^e) = p*(p+1)^(e-1).

%I A348037 #17 Oct 29 2021 09:19:28
%S A348037 1,1,1,2,1,1,1,4,3,1,1,2,1,1,1,8,1,3,1,2,1,1,1,4,5,1,9,2,1,1,1,16,1,1,
%T A348037 1,1,1,1,1,4,1,1,1,2,3,1,1,8,7,5,1,2,1,9,1,4,1,1,1,2,1,1,3,32,1,1,1,2,
%U A348037 1,1,1,1,1,1,5,2,1,1,1,8,27,1,1,2,1,1,1,4,1,3,1,2,1,1,1,16,1,7,3,5,1,1,1,4,1
%N A348037 a(n) = n / gcd(n, A003968(n)), where A003968 is multiplicative with a(p^e) = p*(p+1)^(e-1).
%H A348037 Antti Karttunen, <a href="/A348037/b348037.txt">Table of n, a(n) for n = 1..20000</a>
%F A348037 a(n) = n / A348036(n) = n / gcd(n, A003968(n)).
%F A348037 a(n) = A003557(n) / A348039(n).
%t A348037 f[p_, e_] := p*(p + 1)^(e - 1); a[n_] := n / GCD[n, Times @@ f @@@ FactorInteger[n]]; Array[a, 100] (* _Amiram Eldar_, Oct 20 2021 *)
%o A348037 (PARI)
%o A348037 A003968(n) = { my(f=factor(n)); for (i=1, #f~, p= f[i, 1]; f[i, 1] = p*(p+1)^(f[i, 2]-1); f[i, 2] = 1); factorback(f); }
%o A348037 A348037(n) = (n/gcd(n, A003968(n)));
%Y A348037 Differs from A003557 at the positions given by A347960.
%Y A348037 Cf. A003959, A003968, A333634, A348038, A348039, A348499 (positions of 1's).
%K A348037 nonn
%O A348037 1,4
%A A348037 _Antti Karttunen_, Oct 19 2021