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A348036 a(n) = gcd(n, A003968(n)), where A003968 is multiplicative with a(p^e) = p*(p+1)^(e-1).

%I A348036 #13 Oct 29 2021 09:05:27
%S A348036 1,2,3,2,5,6,7,2,3,10,11,6,13,14,15,2,17,6,19,10,21,22,23,6,5,26,3,14,
%T A348036 29,30,31,2,33,34,35,36,37,38,39,10,41,42,43,22,15,46,47,6,7,10,51,26,
%U A348036 53,6,55,14,57,58,59,30,61,62,21,2,65,66,67,34,69,70,71,72,73,74,15,38,77,78,79,10,3,82,83,42
%N A348036 a(n) = gcd(n, A003968(n)), where A003968 is multiplicative with a(p^e) = p*(p+1)^(e-1).
%H A348036 Antti Karttunen, <a href="/A348036/b348036.txt">Table of n, a(n) for n = 1..20000</a>
%F A348036 a(n) = gcd(n, A003968(n)).
%F A348036 a(n) = gcd(n, A348030(n)) = gcd(A003968(n), A348030(n)).
%F A348036 a(n) = n / A348037(n) = A003968(n) / A348038(n).
%F A348036 a(n) = A007947(n) * A348039(n).
%t A348036 f[p_, e_] := p*(p + 1)^(e - 1); a[n_] := GCD[n, Times @@ f @@@ FactorInteger[n]]; Array[a, 100] (* _Amiram Eldar_, Oct 20 2021 *)
%o A348036 (PARI)
%o A348036 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 A348036 A348036(n) = gcd(n, A003968(n));
%Y A348036 Differs from A007947 at the positions given by A347960.
%Y A348036 Cf. A003959, A003968, A348030, A348037, A348038, A348039.
%K A348036 nonn
%O A348036 1,2
%A A348036 _Antti Karttunen_, Oct 19 2021