A344878 - OEIS

%I #23 Jun 15 2022 14:35:54

%S 1,3,2,7,4,6,6,15,8,12,10,14,12,6,4,31,16,24,18,28,6,30,22,30,24,12,

%T 26,42,28,12,30,63,10,48,12,56,36,18,12,60,40,6,42,70,8,66,46,62,48,

%U 24,16,84,52,78,20,30,18,84,58,28,60,30,24,127,12,30,66,112,22,12,70,120,72,36,24,126,30,12,78,124,80,120

%N a(n) is the least common multiple of numbers (2^(1+e2))-1 and those in the set (p_i^e_i)-1, when the odd part of n = Product (p_i^e_i), and e2 is the 2-adic valuation of n.

%H Antti Karttunen, <a href="/A344878/b344878.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Lc#lcm">Index entries for sequences related to lcm's</a>

%F If n = Product (p_i^e_i), then a(n) = LCM of values (p_i^(e_i+[p==2]))-1, where [ ] is the Iverson bracket.

%F a(n) = lcm(A038712(n), a(A000265(n)).

%F a(n) = A344875(n) / A344879(n).

%t a[n_] := If[n == 1, 1, Module[{p, e}, LCM @@ Table[{p, e} = pe;

%t      (p^(e + If[p == 2, 1, 0])) - 1, {pe, FactorInteger[n]}]]];

%t Array[a, 100] (* _Jean-François Alcover_, Jun 12 2021 *)

%o (PARI) A344878(n) = if(1==n,n, my(f=factor(n)~); lcm(vector(#f, i, (f[1, i]^(f[2, i]+(2==f[1, i]))-1))));

%o (Python)

%o from math import lcm

%o from sympy import factorint

%o def A344878(n): return lcm(*(p**(e+int(p==2))-1 for p, e in factorint(n).items())) # _Chai Wah Wu_, Jun 15 2022

%Y Cf. A000265, A038712, A344875, A344879.

%K nonn

%O 1,2

%A _Antti Karttunen_, Jun 03 2021