A345948 - OEIS

%I #12 Jul 06 2021 20:09:49

%S 1,1,1,1,1,6,1,1,1,4,1,14,1,18,4,1,1,24,1,28,3,10,1,30,1,36,1,14,1,24,

%T 1,1,5,16,12,8,1,54,12,20,1,36,1,70,8,22,1,62,1,72,16,28,1,78,20,18,9,

%U 28,1,56,1,90,24,1,3,12,1,112,11,24,1,120,1,108,24,42,15,72,1,124,1,40,1,84,16,126,28,50,1,96,4,22

%N a(n) = A344875(n) / gcd(A153151(n), A344875(n)).

%H Antti Karttunen, <a href="/A345948/b345948.txt">Table of n, a(n) for n = 1..16384</a>

%H Antti Karttunen, <a href="/A345948/a345948.txt">Data supplement: n, a(n) computed for n = 1..65537</a>

%F a(n) = A344875(n) / A345947(n) = A344875(n) / gcd(A153151(n), A344875(n)).

%F a(2n-1) = A345938(2n-1), for all n >= 1.

%t {1}~Join~Array[#2/GCD @@ {##} & @@ {Which[# < 2, #, IntegerQ[Log2@ #], 2 # - 1, True, # - 1], Times @@ Map[If[#1 == 2, 2^(#2 + 1) - 1, #1^#2 - 1] & @@ # &, FactorInteger[#]]} &, 91, 2] (* _Michael De Vlieger_, Jul 06 2021 *)

%o (PARI)

%o A153151(n) = if(!n,n,if(!bitand(n,n-1),(n+n-1),(n-1)));

%o A344875(n) = { my(f=factor(n)~); prod(i=1, #f, (f[1, i]^(f[2, i]+(2==f[1, i]))-1)); };

%o A345948(n) = { my(u=A344875(n)); (u/gcd(A153151(n), u)); };

%Y Cf. A153151, A344875, A345947, A345949.

%Y Cf. also A345938.

%K nonn

%O 1,6

%A _Antti Karttunen_, Jul 01 2021