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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A360162 a(n) is the sum of the square roots of the unitary divisors of n that are squares. 3
 1, 1, 1, 3, 1, 1, 1, 1, 4, 1, 1, 3, 1, 1, 1, 5, 1, 4, 1, 3, 1, 1, 1, 1, 6, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 12, 1, 1, 1, 1, 1, 1, 1, 3, 4, 1, 1, 5, 8, 6, 1, 3, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 4, 9, 1, 1, 1, 3, 1, 1, 1, 4, 1, 1, 6, 3, 1, 1, 1, 5, 10, 1, 1, 3, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS The number of unitary divisors of n that are squares is A056624(n) and their sum is A358347(n). The unitary analog of A069290. LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 FORMULA a(n) = Sum_{d|n, gcd(d, n/d)=1, d square} sqrt(d). Multiplicative with a(p^e) = p^(e/2) + 1 if e is even, and 1 if e is odd. Dirichlet g.f.: zeta(s)*zeta(2*s-1)/zeta(3*s-1). Sum_{k=1..n} a(k) ~ (3*n/Pi^2)*(log(n) + 3*gamma - 1 - 3*zeta'(2)/zeta(2)), where gamma is Euler's constant (A001620). MATHEMATICA f[p_, e_] := If[OddQ[e], 1, p^(e/2) + 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, f[i, 1]^(f[i, 2]/2) + 1)); } CROSSREFS Cf. A001620, A056624, A069290, A306016, A358347. Sequence in context: A016465 A122947 A367990 * A367988 A363925 A231147 Adjacent sequences: A360159 A360160 A360161 * A360163 A360164 A360165 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 April 12 07:22 EDT 2024. Contains 371623 sequences. (Running on oeis4.)