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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 (list; graph; refs; listen; history; text; internal format)
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))));

CROSSREFS

Cf. A000265, A038712, A344875, A344879.

Sequence in context: A316385 A341911 A341916 * A344875 A178910 A182651

Adjacent sequences:  A344875 A344876 A344877 * A344879 A344880 A344881

KEYWORD

nonn

AUTHOR

Antti Karttunen, Jun 03 2021

STATUS

approved

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Last modified December 9 03:23 EST 2021. Contains 349625 sequences. (Running on oeis4.)