The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A370565 Size of the group Q_3*/(Q_3*)^n, where Q_3 is the field of 3-adic numbers. 6
 1, 4, 9, 8, 5, 36, 7, 16, 81, 20, 11, 72, 13, 28, 45, 32, 17, 324, 19, 40, 63, 44, 23, 144, 25, 52, 729, 56, 29, 180, 31, 64, 99, 68, 35, 648, 37, 76, 117, 80, 41, 252, 43, 88, 405, 92, 47, 288, 49, 100, 153, 104, 53, 2916, 55, 112, 171, 116, 59, 360, 61, 124, 567, 128 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS We have Q_3* = 3^Z X Z_3*, so Q_3*/(Q_3*)^k = (3^Z/3^(kZ)) X (Z_p*/(Z_3*)^k). Note that 3^Z/3^(kZ) is a cyclic group of order k. For the group structure of (Z_3*/(Z_3*)^k), see A370050. LINKS Jianing Song, Table of n, a(n) for n = 1..10000 FORMULA Write n = 3^e * n' with k' not being divisible by 3, then a(n) = n * 3^e * gcd(2,n'). Multiplicative with a(3^e) = 3^(2*e), a(2^e) = 2^(e+1) and a(p^e) = p^e for primes p != 2, 3. a(n) = n * A370180(n). From Amiram Eldar, May 20 2024: (Start) Dirichlet g.f.: ((1 + 1/2^(s-1)) * (1 - 1/3^(s-1))/(1 - 1/3^(s-2))) * zeta(s-1). Sum_{k=1..n} a(k) ~ (n^2/(2*log(3))) * (log(n) + gamma - 1/2 + log(3) - log(2)/3), where gamma is Euler's constant (A001620). (End) MATHEMATICA a[n_] := Module[{e2 = IntegerExponent[n, 2], e3 = IntegerExponent[n, 3]}, 2^Min[e2, 1] * 3^e3 * n]; Array[a, 100] (* Amiram Eldar, May 20 2024 *) PROG (PARI) a(n, {p=3}) = my(e = valuation(n, p)); n * p^e*gcd(p-1, n/p^e) CROSSREFS Row 2 of A370067. Cf. A001620, A370050, A370564, A370566, A370567. Cf. A370180. Sequence in context: A134902 A110992 A199203 * A370567 A371500 A197580 Adjacent sequences: A370562 A370563 A370564 * A370566 A370567 A370568 KEYWORD nonn,easy,mult AUTHOR Jianing Song, Apr 30 2024 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified July 24 22:37 EDT 2024. Contains 374585 sequences. (Running on oeis4.)