A348038 - OEIS

%I #11 Oct 29 2021 09:05:45

%S 1,1,1,3,1,1,1,9,4,1,1,3,1,1,1,27,1,4,1,3,1,1,1,9,6,1,16,3,1,1,1,81,1,

%T 1,1,2,1,1,1,9,1,1,1,3,4,1,1,27,8,6,1,3,1,16,1,9,1,1,1,3,1,1,4,243,1,

%U 1,1,3,1,1,1,3,1,1,6,3,1,1,1,27,64,1,1,3,1,1,1,9,1,4,1,3,1,1,1,81,1,8,4,9,1

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

%H Antti Karttunen, <a href="/A348038/b348038.txt">Table of n, a(n) for n = 1..20000</a>

%F a(n) = A003968(n) / A348036(n) = A003968(n) / gcd(n, A003968(n)).

%F a(n) = A327564(n) / A348039(n).

%t f[p_, e_] := p*(p + 1)^(e - 1); a[n_] := (m = Times @@ f @@@ FactorInteger[n]) / GCD[n, m]; Array[a, 100] (* _Amiram Eldar_, Oct 20 2021 *)

%o (PARI)

%o 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 A348038(n) = { my(u=A003968(n)); (u/gcd(n, u)); };

%Y Differs from A327564 at the positions given by A347960.

%Y Cf. A003968, A005117 (positions of 1's), A327564, A348036, A348037, A348039.

%K nonn

%O 1,4

%A _Antti Karttunen_, Oct 20 2021