This site is supported by donations to The OEIS Foundation.

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A182139 Inverse Moebius transform of A061142 2
 1, 3, 3, 7, 3, 9, 3, 15, 7, 9, 3, 21, 3, 9, 9, 31, 3, 21, 3, 21, 9, 9, 3, 45, 7, 9, 15, 21, 3, 27, 3, 63, 9, 9, 9, 49, 3, 9, 9, 45, 3, 27, 3, 21, 21, 9, 3, 93, 7, 21, 9, 21, 3, 45, 9, 45, 9, 9, 3, 63, 3, 9, 21, 127, 9, 27, 3, 21, 9, 27, 3, 105, 3, 9, 21, 21, 9 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(n) is multiplicative with a(p^e) = -1 + 2^(e+1). If s is squarefree then a(s) = A048691(s). LINKS Enrique Pérez Herrero, Table of n, a(n) for n = 1..5000 FORMULA a(n) = Sum(d|n, 2^Omega(d)) = Sum(d|n, 2^A001222(d)) = Sum(d|n, A061142(d)). EXAMPLE a(12) = a(2^2 * 3^1) = (-1 + 2^(2+1)) * (-1 + 2^(1+1)) = 7 * 3 = 21; or, using the divisors set {1,2,3,4,6,12}: 2^0 + 2^1 + 2^1 + 2^2 + 2^2 + 2^3 = 21. MATHEMATICA t[n_] := DivisorSum[n, 2^PrimeOmega[#]&]; Table[t[n], {n, 100}] CROSSREFS Cf. A001222, A061142, A048691. Sequence in context: A208884 A034257 A145501 * A092693 A134661 A135434 Adjacent sequences:  A182136 A182137 A182138 * A182140 A182141 A182142 KEYWORD nonn,mult AUTHOR Enrique Pérez Herrero, Apr 14 2012 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 January 15 18:42 EST 2019. Contains 319155 sequences. (Running on oeis4.)