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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A166591 Totally multiplicative sequence with a(p) = p+3 for prime p. 18
 1, 5, 6, 25, 8, 30, 10, 125, 36, 40, 14, 150, 16, 50, 48, 625, 20, 180, 22, 200, 60, 70, 26, 750, 64, 80, 216, 250, 32, 240, 34, 3125, 84, 100, 80, 900, 40, 110, 96, 1000, 44, 300, 46, 350, 288, 130, 50, 3750, 100, 320, 120, 400, 56, 1080, 112, 1250, 132, 160 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Vaclav Kotesovec, Table of n, a(n) for n = 1..10000 FORMULA Multiplicative with a(p^e) = (p+3)^e. If n = Product p(k)^e(k) then a(n) = Product (p(k)+3)^e(k). From Vaclav Kotesovec, Feb 11 2023: (Start) Dirichlet g.f.: Product_{p prime} 1 / (1 - p^(1-s) - 3*p^(-s)). Dirichlet g.f.: zeta(s-1) * (1 + 3/(2^s - 5)) * Product_{p prime, p>2} (1 + 3/(p^s - p - 3)). Sum_{k=1..n} a(k) has average order 3 * c * zeta(r-1) * n^r / (5*log(5)), where r = log(5)/log(2) = 2.321928094... and c = Product_{p prime, p>2} (1 + 3/(p^r - p - 3)) = 1.68551448153095... (End) MATHEMATICA f[p_, e_] := (p + 3)^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Vaclav Kotesovec, Feb 11 2023 *) PROG (PARI) a(n) = my(f=factor(n)); for (i=1, #f~, f[i, 1] += 3); factorback(f); \\ Michel Marcus, Jun 09 2014 (PARI) for(n=1, 100, print1(direuler(p=2, n, 1/(1-p*X-3*X))[n], ", ")) \\ Vaclav Kotesovec, Feb 10 2023 CROSSREFS Sequence in context: A047186 A324485 A335827 * A342610 A160529 A039572 Adjacent sequences: A166588 A166589 A166590 * A166592 A166593 A166594 KEYWORD nonn,mult AUTHOR Jaroslav Krizek, Oct 17 2009 EXTENSIONS More terms from Michel Marcus, Jun 09 2014 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 October 2 23:30 EDT 2023. Contains 365841 sequences. (Running on oeis4.)