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

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A056196 Numbers n such that A055229(n) = 2. 2
 8, 24, 32, 40, 56, 72, 88, 96, 104, 120, 128, 136, 152, 160, 168, 184, 200, 224, 232, 248, 264, 280, 288, 296, 312, 328, 344, 352, 360, 376, 384, 392, 408, 416, 424, 440, 456, 472, 480, 488, 504, 512, 520, 536, 544, 552, 568, 584, 600, 608, 616, 632, 640 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS By definition, the largest square divisor and squarefree part of these numbers have GCD = 2. Different from A036966. E.g., 81 is not here because A055229(81) = 1. Numbers of the form 2^(2*k+1) * m, where k >= 1 and m is an odd number whose prime factorization contains only exponents that are either 1 or even. The asymptotic density of this sequence is (1/12) * Product_{p odd prime} (1-1/(p^2*(p+1))) = A065465 / 11 = 0.08013762179319734335... - Amiram Eldar, Dec 04 2020, Nov 25 2022 LINKS Robert Israel, Table of n, a(n) for n = 1..10000 EXAMPLE 88 is here because 88 has squarefree part 22, largest square divisor 4, and A055229(88) = gcd(22, 4) = 2. MAPLE filter:= proc(n) local T; T:= select(t -> (t[2]::odd and t[2]>1), ifactors(n)[2]); nops(T) = 1 and T[1][1]=2; end proc: select(filter, [\$1..1000]); # Robert Israel, Sep 21 2015 MATHEMATICA f[n_] := Block[{p = FactorInteger@ n, a}, a = Times @@ Power @@@ ({#[[1]], Mod[#[[2]], 2]} & /@ p); GCD[a, n/a]]; Position[Array[f, 640], 2] // Flatten (* Michael De Vlieger, Sep 22 2015, after Jean-François Alcover at A055229 *) PROG (PARI) isok(n) = my(c=core(n)); gcd(c, n/c) == 2; \\ after PARI in A055229; Michel Marcus, Sep 20 2015 CROSSREFS Cf. A036966, A055229, A065465. Sequence in context: A227175 A340930 A269420 * A044069 A028628 A333427 Adjacent sequences: A056193 A056194 A056195 * A056197 A056198 A056199 KEYWORD nonn,changed AUTHOR Labos Elemer, Aug 02 2000 EXTENSIONS Edited by Robert Israel, Sep 21 2015 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 December 2 17:33 EST 2022. Contains 358510 sequences. (Running on oeis4.)