The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A056624 Number of unitary square divisors of n. 8
 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 2, 4, 1, 1, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS Unitary analog of A046951. LINKS Antti Karttunen, Table of n, a(n) for n = 1..10000 FORMULA a(n) = 2^r, where r is the number of prime factors of the largest unitary square divisor of n. Multiplicative with a(p^e) = 2^(1-(e mod 2)). - Vladeta Jovovic, Dec 13 2002 Dirichlet g.f.: zeta(s)*zeta(2*s)/zeta(3*s). - Werner Schulte, Apr 03 2018 Sum_{k=1..n} a(k) ~ n*Pi^2/(6*Zeta(3)) + sqrt(n)*Zeta(1/2)/Zeta(3/2). - Vaclav Kotesovec, Feb 07 2019 EXAMPLE n=256, it has 5 square divisors of which only 2,{1,256} are unitary, 3 divisors are not. n=124 has 2 (1 and 4) square divisors, both of them unitary a(124) = 2. n=108 has 12 divisors, 4 square divisors: {1,4,9,36} of which 1 and 4 are unitary, 9 and 36 are not. So a(108)=2. The largest unitary square divisor of 108 is 4 with 1 prime divisor so a(108) = 2^1 = 2. MATHEMATICA Table[DivisorSum[n, 1 &, And[IntegerQ@ Sqrt@ #, CoprimeQ[#, n/#]] &], {n, 105}] (* Michael De Vlieger, Jul 28 2017 *) PROG (Scheme) (define (A056624 n) (if (= 1 n) n (* (A000079 (A059841 (A067029 n))) (A056624 (A028234 n))))) ;; Antti Karttunen, Jul 28 2017 (PARI) a(n) = sumdiv(n, d, if(gcd(d, n/d)==1, issquare(d))); \\ Michel Marcus, Jul 28 2017 CROSSREFS Cf. A000188, A008833, A034444, A046952, A055229, A056626, A059841. Sequence in context: A072170 A294932 A327804 * A193348 A263723 A318498 Adjacent sequences:  A056621 A056622 A056623 * A056625 A056626 A056627 KEYWORD nonn,mult AUTHOR Labos Elemer, Aug 08 2000 EXTENSIONS More terms from Vladeta Jovovic, Dec 13 2002 STATUS approved

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

Last modified October 27 13:45 EDT 2021. Contains 348276 sequences. (Running on oeis4.)