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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.
10
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
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
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jun 03 2021
STATUS
approved