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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A360157 a(n) is the number of unitary divisors of n that are odd squares. 2
 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,9 COMMENTS First differs from A298735 at n = 27. The unitary analog of A298735. The least term that is larger than 2 is a(225) = 4. LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 FORMULA Multiplicative with a(2^e) = 1, and for p > 2, a(p^e) = 1 if e is odd and 2 if e is even. Dirichlet g.f.: (zeta(s)*zeta(2*s)/zeta(3*s)) * (4^s + 2^s)/(4^s + 2^s + 1). Sum_{k=1..n} a(k) ~ c * n, where c = Pi^2/(7*zeta(3)) = 1.172942380817... . More precise asymptotics: Sum_{k=1..n} a(k) ~ Pi^2 * n / (7*zeta(3)) + (4 + sqrt(2)) * zeta(1/2) * sqrt(n) / (7*zeta(3/2)). - Vaclav Kotesovec, Jan 29 2023 MATHEMATICA f[p_, e_] := If[OddQ[e], 1, 2]; f[2, e_] := 1; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] PROG (PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, if(f[i, 2]%2, 1, if(f[i, 1] == 2, 1, 2))); } CROSSREFS Cf. A002117, A013661, A016754, A034444, A056624, A298735. Sequence in context: A031242 A340102 A031260 * A298735 A055090 A290106 Adjacent sequences: A360154 A360155 A360156 * A360158 A360159 A360160 KEYWORD nonn,easy,mult AUTHOR Amiram Eldar, Jan 29 2023 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 August 15 00:19 EDT 2024. Contains 375171 sequences. (Running on oeis4.)