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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A299150 Denominators of the positive solution to n = Sum_{d|n} a(d) * a(n/d). 18
 1, 1, 2, 2, 2, 2, 2, 2, 8, 2, 2, 4, 2, 2, 4, 8, 2, 8, 2, 4, 4, 2, 2, 4, 8, 2, 16, 4, 2, 4, 2, 8, 4, 2, 4, 16, 2, 2, 4, 4, 2, 4, 2, 4, 16, 2, 2, 16, 8, 8, 4, 4, 2, 16, 4, 4, 4, 2, 2, 8, 2, 2, 16, 16, 4, 4, 2, 4, 4, 4, 2, 16, 2, 2, 16, 4, 4, 4, 2, 16, 128, 2, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Antti Karttunen, Table of n, a(n) for n = 1..65537 (first 1000 terms from Andrew Howroyd) FORMULA a(n) = denominator(n*A317848(n)/A165825(n)) = A165825(n)/(A037445(n) * A006519(n)). - Andrew Howroyd, Aug 09 2018 a(n) = A046644(n)/A006519(n). - Andrew Howroyd and Antti Karttunen, Aug 30 2018 From Antti Karttunen, Sep 03 2018: (Start) a(n) = 2^A318440(n). Multiplicative with a(2^e) = 2^A011371(e), a(p^e) = 2^A005187(e) for odd primes p. Multiplicative with a(p^e) = 2^(((1+A000035(p))*e)-A000120(e)) for all primes p. (End) EXAMPLE Sequence begins: 1, 1, 3/2, 3/2, 5/2, 3/2, 7/2, 5/2, 27/8, 5/2, 11/2, 9/4, 13/2, 7/2. MATHEMATICA nn=50; sys=Table[n==Sum[a[d]*a[n/d], {d, Divisors[n]}], {n, nn}]; Denominator[Array[a, nn]/.Solve[sys, Array[a, nn]][[2]]] f[p_, e_] := 2^((1 + Mod[p, 2])*e - DigitCount[e, 2, 1]); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Apr 28 2023 *) PROG (PARI) a(n)={my(v=factor(n)[, 2]); denominator(n*prod(i=1, #v, my(e=v[i]); binomial(2*e, e)/4^e))} \\ Andrew Howroyd, Aug 09 2018 (PARI) A299150(n) = { my(f = factor(n), m=1); for(i=1, #f~, m *= 2^(((1+(f[i, 1]%2))*f[i, 2]) - hammingweight(f[i, 2]))); (m); }; \\ Antti Karttunen, Sep 03 2018 CROSSREFS Cf. A000010, A003958, A005187, A006519, A007431, A011371, A018804, A023900, A029935, A037445, A046643, A046644, A165825, A257098, A298971, A299119, A299149 (numerators), A299151, A317848, A317929, A317932, A318314, A318512, A318653, A318681. Cf. A318440 (the 2-adic valuation). Sequence in context: A140818 A139813 A172009 * A202448 A339165 A129381 Adjacent sequences: A299147 A299148 A299149 * A299151 A299152 A299153 KEYWORD nonn,frac,mult AUTHOR Gus Wiseman, Feb 03 2018 EXTENSIONS Keyword:mult added by Andrew Howroyd, Aug 09 2018 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 September 12 11:52 EDT 2024. Contains 375851 sequences. (Running on oeis4.)