A344878 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.

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

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Index entries for sequences related to lcm's

Formula

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.

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

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

Mathematica

a[n_] := If[n == 1, 1, Module[{p, e}, LCM @@ Table[{p, e} = pe;
     (p^(e + If[p == 2, 1, 0])) - 1, {pe, FactorInteger[n]}]]];
Array[a, 100] (* Jean-François Alcover, Jun 12 2021 *)

Prog

(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))));
(Python)
from math import lcm
from sympy import factorint
def A344878(n): return lcm(*(p**(e+int(p==2))-1 for p, e in factorint(n).items())) # Chai Wah Wu, Jun 15 2022

Crossrefs

Cf. A000265, A038712, A344875, A344879.

Sequence in context: A341916 A360960 A371974 * A344875 A178910 A182651

Adjacent sequences: A344875 A344876 A344877 * A344879 A344880 A344881

Keyword

nonn

Author

Antti Karttunen, Jun 03 2021

Status

approved